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A Location- and Diversity-aware News FeedSystem for Mobile Users

Wenjian Xu, Chi-Yin Chow, Member, IEEE

Abstract—A location-aware news feed (LANF) system generates news feeds for a mobile user based on her spatial preference (i.e.,her current location and future locations) and non-spatial preference (i.e., her interest). Existing LANF systems simply send the mostrelevant geo-tagged messages to their users. Unfortunately, the major limitation of such an existing approach is that, a news feed maycontain messages related to the same location (i.e., point-of-interest) or the same category of locations (e.g., food, entertainment orsport). We argue that diversity is a very important feature for location-aware news feeds because it helps users discover new placesand activities. In this paper, we propose D-MobiFeed; a new LANF system enables a user to specify the minimum number of messagecategories (l) for the messages in a news feed. In D-MobiFeed, our objective is to efficiently schedule news feeds for a mobile user ather current and predicted locations, such that (i) each news feed contains messages belonging to at least l different categories, and(ii) their total relevance to the user is maximized. To achieve this objective, we formulate the problem into two parts, namely, a decisionproblem and an optimization problem. For the decision problem, we provide an exact solution by modeling it as a maximum flowproblem and proving its correctness. The optimization problem is solved by our proposed three-stage heuristic algorithm. We evaluatethe performance of D-MobiFeed using a real data set crawled from Foursquare. Experimental results show that our proposedthree-stage heuristic scheduling algorithm outperforms the brute-force optimal algorithm by at least an order of magnitude in terms ofrunning time and the relative error incurred by the heuristic algorithm is below 1%. D-MobiFeed with the location prediction methodeffectively improves the relevance, diversity, and efficiency of news feeds.

Index Terms—Location-aware news feeds, diversity constraint, online scheduling, location-based services, user mobility

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1 INTRODUCTION

With the advance of wireless communications and the ubiq-uity of GPS-equipped smartphones, social network applicationshave become more prevalent and location-aware, as widelyknown as location-based social networks (LBSNs) (e.g., FacebookPlaces [17] and Foursquare [19]). Anews feedis a commonfunctionality of existing LBSNs. It enables mobile users topostgeo-tagged messages and receive nearby user-generated messagesas news feeds at anytime, anywhere. For example, “Bob canreceive a news feed with 3 messages that are most relevant tohim among the messages within 1 km from his location every10 seconds”. Figure 1a depicts an application scenario. The geo-location of a message could be a point (e.g.,m4), a circularregion (e.g.,m5), or the spatial region of a venue (e.g.,m6 andm7 are spatially associated with restaurantR1). Besides, geo-tagged messages can be categorized by their underlying venues;for instance,m6 andm7 are posted from users at restaurantR1,so they are intuitively categorized to a “restaurant” category.

Our previous work developed MobiFeed [39]; the state-of-the-art location-aware news feed system schedules news feeds formobile users. In MobiFeed, the relevance of a messagem to Bobis measured by both the content similarity betweenm and Bob’ssubmitted messages (i.e., a non-spatial factor) and the distancebetweenm and Bob (i.e., a spatial factor). MobiFeed is motivatedby the fact that, if the news feeds are only computed based ona user’s location at the query time (i.e., it does not consider theuser’s future locations, e.g., GeoFeed [7]), the overall relevance

• W. Xu and C.-Y. Chow are with the Department of Computer Science, CityUniversity of Hong Kong, Hong Kong.E-mail: wenjianxu2-c@my.cityu.edu.hk, chiychow@cityu.edu.hk

of news feeds is not optimized. For example, in Fig. 1a, thereare11 messages (i.e.,m1 to m11) with their geo-location intersectingBob’s query regions (i.e., circular regions in Fig. 1a) at timet0, t1,and/ort2. Assumemi is more relevant to Bob thanmj if i < j,and the number of messages per news feed (i.e.,k) is 3. GeoFeedreturns (m1, m2, m3) at t0, (m4, m6, m7) at t1, and (m5) att2. To improve the relevance of news feeds, given Bob’s currentlocation att0, MobiFeed predicts two future locations for him att1 andt2, andschedulesnews feeds by considering all three queryregions at the same time, which results in a better solution with(m1, m2, m3), (m4, m8, m9), and (m5, m6, m7) at t0, t1 andt2,respectively. In summary, MobiFeed aims at maximizing thetotalrelevanceof generated news feeds by utilizinglocation predictiontechniques.

Unfortunately, relevance alone is unable to capture the broaderaspects of user satisfaction. Although users expect to receivemessages that are highly relevant to their interests, they mayprefer a location-aware news feed with a certain level of diversity(i.e., the messages in a news feed belong to a certain number ofcategories). In conventional web search or recommender systems,topic diversification is a key method to improve user satisfac-tion [2], [3], [37], [42]. This work considers a mobile environmentthat makes our location- and diversity-aware news feed systemunique and more challenging. With the geographical distancebetween a message and a mobile user in a relevance measuremodel, the relevance of a message to a mobile user is changingas the user is moving. Such a dynamic environment gives us anopportunity to employ location prediction technique to improvethe quality of news feeds and the system efficiency.

To show the limitation in our previous model MobiFeed, wehave conducted experiments to investigate the diversity ofits newsfeeds generated for mobile users. Experimental results show that,

2

Shopping Mall S1 (m1, m2, m3)

1.xxx2.xxx3.xxx

Bob at time t0Hotel H1 (m8, m9)

Restaurant R2 (m10, m11)

m4 with alocationpoint

m5 with acircular region

D

A predicted location for Bob at time t2=t0+2×td

A predictedlocation forBob at timet1=t0+td Message Category Message content

m1 Shopping

Blanches, the cafe on thetop floor, is great forlunch or a quick snackwhile shopping

m2 ShoppingI just love their sales. Idid my Xmas shoppingthere & only spent $50.

m3 Shopping

This is one of ourfavorite shoppingdestinations in NYC.They also have ourfavorite windows duringthe holidays. And theyhave the nicest publicrestrooms.

(a) (b)

Restaurant R1 (m6, m7)

m5m6m7m8

Message

m1m2m3

m9m10m11

m4MuseumRestaurantRestaurantHotel

Category

ShoppingShoppingShopping

HotelRestaurantRestaurant

Cinema

Category information

Fig. 1: (a) An application scenario. (b) The news feed att0 generated by MobiFeed.

0

20

40

60

80

100

1 2 3 4 5

New

s F

eeds

(%

)

No. of Categories

(a) Distribution of news feeds withdifferent numbers of categories (k =5)

0.0

0.5

1.0

1.5

2.0

1 2 3 4 5 6 7 8 9 10

No.

of C

ateg

orie

s pe

r N

ews

Fee

d

No. of Messages per News Feed

(b) The number of categories in newsfeeds with variousk

Fig. 2: Diversity of news feeds generated by MobiFeed.

whenk = 5, over 75% news feeds contain messages belongingto one category and about 20% of news feeds are related to twocategories; over 95% of news feeds are related to only one or twocategories, as depicted in Figure 2a. Even ifk is increased to 10,the diversity of the news feeds generated by MobiFeed is still verylow (i.e., the average number of categories is two), as showninFigure 2b.

To this end, we propose D-MobiFeed, a framework that takesboth the relevance and diversity of news feeds into account whenscheduling news feeds for moving users. In particular, we addan l-diversity constraint into MobiFeed; this constraint requiresthat messages in a news feed belong to at leastl distinct messagecategories. Thisl-diversity constraint brings a brand new challengeto D-MobiFeed, i.e.,the trade-off between relevance and diversityof news feeds. Consider the same example in Fig. 1a, the categoryinformation table depicts the category of each message (e.g.,m1, m2, and m3 belong to the “shopping” category andm4

belongs to the “cinema” category). With a3-diversity constraint,D-MobiFeed returns a solution with (m1, m4, m10), (m2, m6,m8), and (m3, m5, m7) at t0, t1 andt2, respectively. Comparedto MobiFeed, the relevance of the news feeds generated by D-MobiFeed is slightly degraded. Despite that, users may still preferthe news feeds with a higher level of diversity, as shown in theresult of user studies performed by Ziegler et al. [42]. As aresult, the challenge of D-MobiFeed is:how to effectively schedulelocation- and diversity-aware news feeds for mobile users whilemaintaining their high relevance to the users at the same time?

In this paper, we aim at designing D-MobiFeed by furtherconsidering the diversity in news feeds to address this challenge.

Specifically, D-MobiFeed is composed of four key functions:loca-tion prediction, relevance measure, l-diversity constraint checkerandnews feed scheduler. As shown in Figure 1a, given a useru’slocation at current timet0, minimum message display timetd,range distanceD, the requested number of messages per newsfeed k, the minimum number of categoriesl, and a system-specified look-ahead stepsn, the location prediction functionestimatesn future locations foru at timest1 = t0 + 1 × td,t2 = t0 + 2 × td, . . . , andtn = t0 + n × td, the relevancemeasurefunction computes the relevance score of each candidatemessage with a geo-location intersecting anyu’s query region (i.e.,circular regions in Figure 1a). After that, thel-diversity constraintcheckerdecides whether the system could compute news feedsfrom the candidate messages foru’s query regions att0, t1, . . . ,tn, such that messages in each news feed belong to at leastlcategories. Thisl-diversity constraint checking is referred to asa decision problem. Finally, the news feed schedulergeneratesn + 1 news feeds satisfying thel-diversity constraint, and theirtotal relevance score is maximized. The problem of maximizingthe total relevance score is referred to as anoptimization problem.The computedn + 1 news feeds are sent tou. u’s mobile deviceimmediately displays the first news feed (i.e., the one generatedfor the query region att0), and then displays each of the remainingnews feeds one by one for everytd.

To the best of our knowledge, this is thefirst study toincorporate both relevance and diversity for scheduling location-aware news feeds for mobile users in LBSNs. In general, the keycontributions of this work can be summarized as follows:

• We extend our previous model MobiFeed (i.e., the state-of-the-art location-aware news feed system) to consider boththe relevance and diversity of news feeds when generatingnews feeds for mobile users.

• We model thedecision problemas a maximum flowproblem to find the minimum total diversity of a set ofn + 1 news feeds for a user based on the user-specifiedl-diversity constraint. (Section 5)

• We propose a three-stage heuristic approach to solve theoptimization problem. The first stage solves a minimumcost flow problem to guarantee the minimum total diversityin a set ofn+1 news feeds. The second stage addresses areplenish-up-to-k problem to maximize the total relevanceof these news feeds. The last stage simply sorts the

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messages in each news feed. (Section 6)• We conduct extensive experiments to evaluate the per-

formance of D-MobiFeed using a real LBSN data setcrawled from Foursquare in terms of relevance, diversity,and efficiency. (Section 7)

The rest of the paper is organized as follows. We highlightrelated work in Section 2. We describe the system model ofD-MobiFeed in Section 3. Section 4 gives an overview of D-MobiFeed. In Sections 5 and 6, we present our solutions for thedecision problem and the optimization problem, respectively. Sec-tion 7 evaluates the performance of D-MobiFeed through extensiveexperiments. Finally, we conclude this paper in Section 8.

2 RELATED WORK

In this section, we highlight the state-of-the-art techniques inlocation-aware news feed systems and existing diversity modelsin recommender systems and web search systems.

Location-aware news feed systems.Most existing newsfeed systems only provide publish/subscribe services thatsimplyforward messages to subscribed users [10], [35]. Bao et al. [7]injected the location-awareness into a news feed system, whichenables a message to be associated with a spatial extent tocontrol where users can receive it. We proposed a frameworkMobiFeed [39] that is designed to schedule news feeds for mobileusers. MobiFeed takes the limitations of mobile devices andtheuser’s preferences into account, and schedules the mostrelevantgeo-tagged messages to mobile users. Unfortunately, MobiFeedhas a major limitation that only considers the relevance of mes-sages to users, so a news feed may contain messages related tothesame category; and thus it would impede users to discover newplaces and activities. In conventional web search/recommendersystems, topic diversification is a key method to improve usersatisfaction [2], [3], [37], [42]. To address this limitation, our D-MobiFeed framework allows users to specify their required levelsof diversity of news feeds in terms of the number of messagecategories (i.e., thel-diversity constraint). D-MobiFeed aims atmaximizing the total relevance of news feeds and satisfyingthecondition that each news feed contains messages belonging to atleastl categories.

l-diversity principle for privacy-preserving data pub-lishing. The l-diversity principle [28] is proposed for privacy-preserving data publishing. Basically, this principle is used to gen-eralize non-sensitive attributes (e.g., zip codes 13053 and 13068are generalized to “130**” and ages 28, 29, and 21 are generalizedto “< 30”) in a class of records such that the sensitive attributeachieves thel-diversity constraint, in order to protect the privacyof published data. The entropyl-diversity is further used to defendagainst the homogeneity problem without considering the role ofbackground knowledge, i.e., entropy increases as frequencies ofsensitive attributes become more uniform. In this work, we focuson a different problem because D-MobiFeed aims to maximizethe relevance of news feeds for mobile users while news feedssatisfy thel-diversity constraint (i.e., the messages in each newsfeed belong to at leastl categories).

Diversity-aware recommender systems.In MobiFeed [39],the only metric used to evaluate its quality as a recommendersystem is the relevance of messages to users (i.e., accuracy). How-ever, it is argued in [30] that, developing recommender systemswith accuracy as the single goal has many drawbacks, and therecommender community should move beyond the conventional

accuracy metrics. One promising direction that has drawn recentinterest is to diversify the recommendation lists [4]. Ziegler etal. [42] proposed anintra-list similarity metric to measure theoverall diversity of a recommendation list, where the similaritybetween products is derived from their taxonomy-based catego-rization. The authors employed a heuristic algorithm to increasethe diversity of a recommendation list, and their user studyresultsshow that in spite of the loss in accuracy, users still preferthe rec-ommended items with larger extent of diversity. Zhang et al.[41]addressed the diversification problem as the joint optimizationof two objective functions (i.e., the relevance and diversity of arecommendation list), which is solved by using binary quadraticprogramming algorithms.

Diversity-aware web search systems.The process of websearch systems differs from that of recommender systems since itinvolves an explicit user query (i.e., keywords). The query, how-ever, is also ambiguous and has more than one interpretation[34].One possible way to address this problem is to produce a set ofdiversified results that cover different interpretations of the targetquery. Specifically, the search result diversification approaches inthe literature can be classified as eitherimplicit or explicit. Implicitapproaches [8], [40] assume that similar documents will coversimilar aspects of a query. Their basic idea is to iteratively selectdocuments which are similar to the query but different to thealready selected ones in terms of vocabulary [8] or divergencein language models [40]. Explicit approaches [5], [9], on theother hand, model aspects of a query in an explicit approach.For example, Agrawal et al. [5] assumed that there exists aclassification taxonomy over queries and documents to representuser intentions, and they proposed a diversification function thatmaximizes the probability of finding at least one relevant docu-ment in the top-k positions. Similarly, Carterette and Chandar [9]modeled the aspects of a query as topics extracted from the topranked documents, and they designed a probabilistic methodtomaximize the coverage of the retrieved documents.

The above-mentioned diversity-aware recommender systemsand web search systems focus on retrieving an individual list ofitems with a certain level of diversity, in order to improve usersatisfaction. In this work, we focus on a mobile environment,where mobile users are moving in a road network. Our problemis unique and more challenging as D-MobiFeed considers the ge-ographical distance factor between messages and mobile users inthe relevance measure model, and thus, the relevance of messagesto users could be changing as they are moving. In addition, D-MobiFeed has an opportunity to employ a location predictiontechnique to improve the quality of news feeds by schedulingmultiple (i.e., n + 1, wheren is a look-ahead step) location-and diversity-aware news feeds for mobile users simultaneously.The main reason is that computing each news feed individuallyas in the web search or recommender systems will not maximizethe total relevance of news feeds for a user. In our experimentalresults, as depicted in Section 7, D-MobiFeed withn = 0generating a news feed at a time performs worse than D-MobiFeedwith n > 0 computing a set ofn news feeds simultaneously, interms of relevance, diversity, and efficiency.

3 SYSTEM MODEL

In this section, we present the system model of D-MobiFeed.

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User uat time t0

u att1=t0+td

m5m4

{m1, m2, m3}

{m6, m7, m8, m9}

{m10, m11}

Venue C

Venue A

Venue B

u att2=t0+2×td

Message CategoryRelevance score

to u

m1 Restaurant 0.58

m2 Restaurant 0.58

m3 Restaurant 0.33

m5 Theater 0.53m6 Shopping 0.3

m7 Shopping 0.4

m8 Shopping 0.5

m9 Shopping 0.5

m10 Museum 0.55

m11 Museum 0.5

Table I. Candidate messages at t0

Message CategoryRelevance score

to u

m1 Restaurant 0.68

m2 Restaurant 0.68

m3 Restaurant 0.43

m4 Stadium 0.4

m5 Theater 0.15

Table II. Candidate messages at t1

Message CategoryRelevance score

to u

m1 Restaurant 0.35

m2 Restaurant 0.35

m3 Restaurant 0.1

m4 Stadium 0.53

Table III. Candidate messages at t2

(b)(a)

Fig. 3: (a) An example. (b) Three sets of candidate messages associated with their category and relevance score tou.

Category-associatedGeo-tagged Messages

M

Query

News Feed

1.xxx2.xxx3.xxx4.xxx

Mobile User

Location-Aware NewsFeed Scheduler

LocationPrediction

RelevanceMeasure

Server

l-Diversity ConstraintChecker

Fig. 4: System architecture of D-MobiFeed.

3.1 System Architecture

Figure 4 depicts the system architecture of D-MobiFeed, which isdesigned based on the framework in [39]. D-MobiFeed consists oftwo major entities.

Category-associated geo-tagged messages.We useM todenote the message collection in D-MobiFeed. Each messagemj ∈ M is defined as a tuple (MessageID, SenderID, Content,Timestamp, Spatial, Category), where MessageIDis a messageidentifier,SenderIDis its sender’s identifier,Contentis its content,Timestampis its post time,Spatial is its spatial extent, andCategory is its category. D-MobiFeed supports three types ofspatial extent, namely, points, regions, and venues. As ourrunningexample depicted in Figure 3a,m4 is geo-tagged by a circularregion,m5 is geo-tagged by a point location, and{m1,m2,m3},{m6,m7,m8,m9}, and{m10,m11} are geo-tagged with venuesA, B, and C (represented by rectangles), respectively. In D-MobiFeed, each message is associated with exactlyonecategory,and setC = {c1, c2, . . . , ch} denotes all categories. If the explicitcategory of messages is not available, clustering methods can beapplied to assign a category for each message [38]. Figure 3bshows the category for each message in our running example.

System users.In D-MobiFeed, a mobile useru equipped witha GPS-enabled mobile device can post a new message taggedwith a spatial extent. A location- and diversity-aware newsfeedquery consists of four parameters: (1) the number of messagesin a news feed (k), (2) the minimum number of categories forthe messages in a news feed (l), (3) the message display time fora news feed (td), and (4) a query range distance (D). The useris able to specify these four query parameters based on his/herpreferences. In practice, the system could provide defaultvalues

for these query parameters. For example, the simplest way isto setthese parameters to the most common values or the average values.In other words, the user is able to receive at mostu.k messageswithin her specified range distanceu.D (i.e., the query region of anews feed) as a news feed. D-MobiFeed computes a news feed foru by selecting messages based on their category, their relevance tou andu’s movement. Since the user needs some time to read themessages, each news feed will be displayed onu’s mobile devicefor a time periodu.td. Note that each message can be displayedto a user only once. Assume the look-ahead step isn, u reports itslocation to the server at every time period(n + 1) × u.td. Afterreceivingu’s location update,n+ 1 news feeds are computed foru. u’s mobile device immediately displays the first news feed, andthen displays each of the remaining news feeds one by one foreveryu.td.

3.2 Location Prediction and Relevance Measure

In this subsection, we describe thelocation predictionand rele-vance measurefunctions in D-MobiFeed.

3.2.1 Location PredictionThe location predictionfunction can employ any existing locationprediction algorithm if it can predict a user’s location at aspecifiedfuture time in a road network. In the experiments (Section 7), weincorporate the path prediction algorithm [26] into D-MobiFeed.Given a useru’s current location,u’s historical trajectories, theroad map, and a future timet, the path prediction algorithmestimatesu’s location att. For the technical detail of the predictionalgorithm employed in D-MobiFeed, please refer to [26].

3.2.2 Message Relevance MeasureD-MobiFeed only requires therelevance measurefunction toreturn a score to indicate the relevance of a messagemj to auserui, i.e., relevanceScore(ui,mj). We combine the followingnon-spatial and spatial factors to implement therelevance measurefunction.

Message contents.The user may be more interested in mes-sages that are similar to his or her submitted ones (e.g., a user’scommon keywords reflect his or her interests [33]). For example,a user issued a message “I like spicy food” would be happy toreceive messages about Thai restaurants. Therefore, we usevector

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space model [29] to measure the relevance of a message to aparticular user in terms of content similarity. Specifically, let Tdenotes the term set of the message setM, and each messagemj is represented as a vector of weights of all terms inT , i.e.,mj .V = 〈wj1, wj2, . . . , wj|T |〉. In general, a termTk ∈ Tshould be weighted higher formj if Tk occurs more frequently inmj and occurs rarely in other messages inM. The weight can becomputed by theTF×IDF scheme:wjk = tfjk·log

|M|dfk

, wheretfjk is the term frequencyof Tk in mj anddfk is thedocumentfrequencyof Tk in M. To incorporate the vector space model intoD-MobiFeed, we maintain a query vector for each user based onher submitted messages. Given a querying userui with a queryvectorui.V and a messagemj , we use the cosine similarity to

computecontentScore(ui,mj) =∑|T |

k=1wik·wjk

√

∑|T |k=1

w2

ik·√

∑|T |k=1

w2

jk

, where

wik ∈ ui.V andwjk ∈ mj.V .Distance.We argue that the geographical proximities between

users and messages have a significant influence on the relevancemeasure. In our scenario, the relevance of a messagemj to a userui can be measured by their distance, i.e.,Dist(ui,mj). If mj isassociated with a circular region or a venue,Dist(ui,mj) returnstheminimumdistance betweenui and the spatial extent ofmj . Toaccommodate the difference in the value ranges ofDist(ui,mj)and other relevance measures, we normalizeDist(ui,mj) to befrom zero to one, i.e.,NDist(ui,mj) = 1 −

Dist(ui,mj)u.D

, whereu.D is the query range distance of a news feed.

Relevance measure function.We employ a linear combina-tion method to integrate the aforementioned two factors into therelevance measurefunction [11]. Specifically, we have:

relevanceScore(ui,mj) =contentScore(ui,mj)× (1 − β)

+ NDist(ui,mj)× β (1)

where0 ≤ β ≤ 1 andβ is a parameter that gives a weight forthe importance of the distance factor with respect to the contentsimilarity factor. Thus, we ensure thatrelevanceScore(ui,mj) isbetween zero and one. In practice, as the D-MobiFeed modeldepicted in Figure 4, the relevance measure function is separatedfrom the core location-aware news feed scheduler. Any relevancemeasure function which returns a numeric score as an output canbe used in D-MobiFeed.

Figure 3b directly gives the computed relevance score of eachmessage for the user. The detailed score computation of thisexam-ple can be found in [39]. Note that since we consider the distancebetween a message and a user as one of the factors in the relevancemeasure, the relevance of a message to a user could vary at differ-ent locations. In our example,relevanceScore(u,m1) = 0.58 att0 while relevanceScore(u,m1) = 0.68 at t1.

4 SYSTEM OVERVIEW

In this section, we give a system overview of D-MobiFeed bydefining key problems in each of its three major steps, namely,candidate message step, decision step, and scheduling step, asdepicted in Figure 5, and showing how these steps interact withthe four key functions, i.e.,location prediction, relevance measure,l-diversity constraint checker, andnews feed scheduler.

Candidate message step.Given a useru’s location at currenttime t0, u’s specified minimum message display timetd, u’srequired range distanceD, u’s requested number of messages pernews feedk, u’s specified minimum number of categoriesl, the

location predictionfunction (see Section 3.2.1) returnsn future lo-cations at timest1, t2, ...tn for u, whereti = t0+i×td. Then thenews feed schedulergeneratesn+1 query regions centered at eachlocation (i.e., one reported location andn predicted locations). Foreach query region atti, a range query is issued to retrieve a setof candidate messagesCandidateMsgi with their spatial extentintersecting the query region. After that, therelevance measurefunction (see Section 3.2.2) calculates a relevance score for eachmessage inCandidateMsgi to u.

Decision step.After thecandidate message step, we haven+1 sets of candidate messages associated with their category andrelevance score tou (e.g., Figure 3b for our running example).The l-diversity constraint checkernow decides whether we couldgeneraten+1 news feeds from the candidate message sets, underthe constraint that messages in each news feed belong to at leastlcategories. This decision problem is defined as follows:

Definition 1. l-Diversity Constraint Checking (DCC) Problem:Given a useru’s news feed query and a look-ahead stepn, D-MobiFeed decides whether it could schedule at most k messagesfor each ofn + 1 news feeds, such that messages in each newsfeed belong to at leastl categories.

The details of how to address this decision problem will bedescribed in Section 5. If the result of DCC is positive (i.e., eachnews feed of a set ofn+ 1 news feeds can satisfy thel-diversityconstraint), D-MobiFeed proceeds to perform the scheduling step.Otherwise, thel-diversity constraint checkerreturns a value ofγ for the news feed scheduler, where γ is the minimum totaldiversity of a set ofn+ 1 news feeds.

Definition 2. Minimum Total Diversity (γ): Given a set ofn+ 1news feeds and anl-diversity constraint, the minimum total di-versity (γ) is the sum of (1) the maximum number of categories(which is less thanl) of a news feed that cannot satisfy thel-diversity constraint and (2) the minimum number of categories(which is equal tol) of a news feed that can satisfy thel-diversityconstraint. If every news feed can satisfy thel-diversity constraint,γ = l× (n+1). However, if at least one news feed cannot satisfythe l-diversity constraint,γ < l × (n+ 1).

Scheduling step.The news feed schedulercomputesn + 1news feeds that satisfy theminimum total diversity(γ) andhave themaximum total relevance score. D-MobiFeed supportsdifferent weights for different positions in a news feed result list,i.e., a higher weight is given to a message displayed at a higherposition because it would be easier to draw a user’s attention [39].Specifically, given a result list withk positions, the weight of thefirst position isk, the weight of the second position isk − 1, andso on. In general, the weight of a messagemj at thej-th position(1 ≤ j ≤ k) is displayWeight(j, k) = k − (j − 1). Thus, therelevance score of a news feedf with k messagesm1, m2, . . . ,mk is calculated as:

relevanceScore(f) =k∑

j=1

relevanceScore(u,mj)

× displayWeight(j, k), (2)

where the sum of the relevance scores ofn + 1 news feeds isthe total relevance score of a query answer. Maximizing suchatotal relevance score is an optimization problem that is defined asfollows:

6

u issues a query

Location prediction

function returns n

future locations

News feed

scheduler processes

n+1 range queries

Relevance measure

function calculates

relevance scores

n+1 sets of

candidate

messages

News feed scheduler computes news

feeds that (a) satisfy the minimum

total diversity (g) and (b) have the

maximum total relevance score

n+1 news feeds

for u

Candidate message

step

Scheduling step Decision step

L-diversity constraint checker

determines the minimum total

diversity (g) for n+1 news feeds

Fig. 5: The work flow of D-MobiFeed.

Definition 3. l-Diversity Constrained News Feed Scheduling(DCS) Problem: Given a useru’s news feed query and a look-ahead stepn, D-MobiFeed schedules at mostk messages for eachof n + 1 news feeds, such that (O1) messages in each news feedbelong to at leastl categories, and (O2) the total relevance scoreof the generated news feeds is maximized.

The details of this problem will be discussed in Section 6.Consider our running example in Figure 3a, wheren = 2, k =4, and l = 3. Note that when we discuss these two problems(Definitions 1 and 3) using this example in the next two sections,we assume that we have already finished thecandidate messagestep and got three sets of candidate messages along with theircategory and relevance score to the user (Figure 3b).

Finally, we discuss how thenews feed schedulerdeals with aninaccurate predicted location. A tolerance thresholdθ is definedfor the difference between a user’s actual location and its cor-responding predicted location for a query region. If the locationdeviation is larger thanθ, a prediction error occurs, andu reportsits actual location to the server to retrieve a new set of newsfeeds.For example, for a trajectory with a user’s locations at times t0,t1 = t0 + td, t2 = t0 + 2 × td, . . . , wheretd is the minimumdisplay time, a first call of 2-look-ahead scheduling att0 generatesnews feeds fort0, t1, andt2. If no prediction error occurs fromt0to t2, a second call of scheduling will take place att3. In contrast,if a prediction error occurs att1, our schedule will perform re-scheduling att1 and re-generate news feeds fort1, t2, and t3.To reduce communication overhead, we determine (i) a set of newmessages that are in a newly computed set of news feeds, but not ina previous set of news feeds, and (ii) positive or negative updatesindicate that a certain message should be added to or removedfrom the previous result lists, respectively [31]. D-MobiFeed onlysends the set of new messages, positive and negative updatestothe user. In practice,θ can be set to the accuracy of the underlyingpositioning technique and device. For example, if assisted-GPS isused,θ is set to 50 meters [15].

5 l-DIVERSITY CONSTRAINT CHECKING

The l-Diversity Constraint Checking (DCC) problem is non-trivial. Using a brute-force method to find an exact solutionhasto try all possible combinations of news feeds forn + 1 newsfeeds. Such a brute-force method is too costly for our onlinescheduling problem. To this end, we model the DCC problem as amaximum flow problem and prove the exactness and correctnessof the model. Finally, the DCC problem returns the minimum totaldiversityγ (Definition 2) as an input for the scheduling step (seeFig. 5). In the next section (i.e., Section 6), we will describe howthe scheduling step computes a set of news feeds that satisfythe

minimum total diversity and have the maximum total relevancescore.

5.1 Maximum Flow Model

The DCC problem is equivalent to the following reduced problemin terms of the result (i.e., given the same input, if the originalproblem has a positive (respectively, negative) answer, the reducedproblem also has a positive (respectively, negative) answer, andvice versa):

Definition 4. Reducedl-Diversity Constraint Checking (RDCC)Problem: Givenn + 1 sets of candidate messages foru’s queryregions at t0, t1, t2, . . . , and tn (i.e., CandidateMsgi, where0 ≤ i ≤ n), along with their category, D-MobiFeed decideswhether it could schedulen + 1 news feeds such that each newsfeed contains exactlyl messages, and each message belongs to adistinct category.

The RDCC problem can be modeled as themaximum flowproblem [6]. Consider our example in Figure 3, wheren = 2,l = 3, and three sets of candidate messages are available foru’squery region att0, t1, andt2. This RDCC problem is representedby a flow graphdepicted in Figure 6. The flow graph consists ofthree sets of nodes:

• Nr representsn + 1 news feeds, wheren is the numberof look-ahead steps. In our example,Nr = {r0, r1, r2}.

• Nc is divided inton + 1 groups, and each group is com-posed of all the categories for messages in correspondingcandidate message set. In our example, ‘Restaurant’ (Re),‘Theater’ (Th), and ‘Museum(Mu)’ are three nodes in thefirst group ofNc since they are the categories for messagesin CandidateMsg0.

• Nm stands for the set ofdistinct messages in allCandidateMsgi, where0 ≤ i ≤ n. There are eleven nodes(m1 to m11) belonging toNm in our example.

Furthermore, we add two extra nodes, namely, the sources andthe sink t, in the flow graph. LetV be the set of nodes in thegraph, i.e.,V = Nr ∪Nc ∪Nm ∪{s, t}. Each nodev ∈ V has abalanceb(v) [6]. For everyri ∈ Nr, cj ∈ Nc andmk ∈ Nm, thebalance is set to 0. Fors andt, b(s) = γ andb(t) = −γ, whereγ is thevalue of flowwe want to maximize. In our example, thebalances are shown on the top of each set of nodes in Figure 6.LetE be the set of edges in the flow graph. Each edgee(vi, vj) ∈E is associated with acapacity c(vi, vj). The set of edgesEcomprises: (1) an edgee(s, ri) for every news feedri ∈ Nr,with capacityl (e.g.,l = 3 in our example), (2) an edgee(ri, cj)between every news feedri ∈ Nr and the categories of messages

7

s

r0

r1

Re

Th

Mu

t

Re

St

Th

m2

m3

m4

m5

m9

m10

m1

m11

r2

Re

St

Sh

m7

m6

m8

Nodes from Nr Nodes from Nc Nodes from Nm

Re-Restaurant

Th-Theater

Mu-Museum

St-Stadium

Sh-Shopping

3 (0)

1 (0)

1 (wjk)

1 (0)

b = g

b = 0 b = 0 b = 0

b = -g1st group

2nd group

3rd group

Fig. 6: Flow graph representation of the RDCC problem (Defini-tion 4) and theγ-Selection problem (Definition 5). All the edgesin the graph have capacity 1 except the edges between source nodes and nodes fromNr. The value in parentheses indicates the costof edges for the representation of theγ-Selection problem.

in CandidateMsgi in Nc, with capacity 1 (e.g., in our example,r0 links to the nodes representing ‘Restaurant’, ‘ Theater’, and‘Museum’ in the first group ofNc), (3) an edgee(cj,mk) forevery categorycj ∈ Nc (cj is assumed in(i + 1)-th group ofNc) linking to messagemk ∈ CandidateMsgi which belongs tocategorycj , with capacity 1 (e.g., in Figure 6, for the category‘Restaurant’ in the first group ofNc, it connects tom1, m2, andm3), and (4) an edgee(mk, t) for every messagemk ∈ Nm, withcapacity 1. In Figure 6, the label on the top of each set of edgesindicates their edge capacity.

Given the above graph, themaximum flow problemis to assignan integerflow valuex(vi, vj) ∈ [0, c(vi, vj)] for each edgee(vi, vj) ∈ E such that for every nodev ∈ V , the followingflow conservation propertyholds:

∑

e(v,vi)∈E

x(v, vi)−∑

e(vi,v)∈E

x(vi, v) = b(v), (3)

and the value of the flow (i.e.,γ) is maximized, that is, we wantto route as much flow as possible froms to t.Solution. The maximum flow problem and its applications are ex-tensively discussed in [18] and [16]. Apart from the classical algo-rithms, many others, such as binary blocking flow algorithm [22]and push-relabel method [23], have been proposed to efficientlysolve the maximum flow problem. We employ the relabel-to-frontalgorithm [12], which is a particular implementation of thepush-relabel method. This algorithm runs in timeO(V 3), whereV isthe number of nodes in the flow graph.

5.2 Correctness Proof

After solving the above maximum flow problem, we obtain theoptimalvalue of flow (i.e.,γ). We interpret this value as follows1:

Theorem 1. (i) If γ = (n+ 1)× l, l-diversity constraint can besatisfied for a news feed query.(ii) If γ < (n + 1) × l, l-diversity constraint cannot be satisfied

1. The value ofγ cannot be larger than(n+1)×l according to the modellingof the flow graph in Section 5.1.

for a news feed query. However,γ indicates the minimum totaldiversity for thesen+ 1 news feeds, as defined in Definition 2.

Proof. Given the graph modelling of the RDCC problem (seeFigure 6), since the capacityc(mk, t) for everymk ∈ Nm is setto 1, it ensures that every message can be scheduled at most once.With the edges between nodes inNc and nodes inNm, everymessage is associated with its corresponding category. Besides,since the capacityc(ri, cj) with ri ∈ Nr andcj ∈ Nc is set to1, it guarantees that for each news feed, D-MobiFeed can select atmost one message for each category. Finally, because we set thecapacity of source edges (i.e.,c(s, ri) for everyri ∈ Nr) as l, itensures that when a news feed already contains messages withl

distinct categories, scheduling more messages with new categoriesdoes not contribute to the optimal value of the flow (i.e.,γ).

For the case (i), if theoptimal value of flow (i.e.,γ) equals(n + 1) × l, all the source edges are saturated (i.e.,x(s, ri) = lfor each edge(s, ri)). It means that for each ofn+1 news feeds,D-MobiFeed could schedule exactlyl messages, with each onebelonging to a distinct category. Therefore,l-diversity constraintcan be satisfied for current news feed query.

For the case (ii), ifγ < (n + 1) × l, one or more sourceedges are not saturated; it corresponds to the fact that at leastone news feed cannot satisfy thel-diversityconstraint. However,as weexactly solve the maximum flow problem formulated inSection 5.1, the value ofγ is maximized. That is,γ is the largestvalue of the minimum total diversity for then + 1 news feeds(Definition 2).

For the example in Figure 3, when we apply the relabel-to-front algorithm to the flow graph in Figure 6, the optimal valueof flow γ is 7 < (n + 1) × l = 9, which means D-MobiFeedcannot schedule three news feeds such that each of them satisfiesthe 3-diversityconstraint. However, we ensure that the minimumtotal diversity for these three news feeds is 7.

5.3 Discussion

Here we give some discussions about the relationship between thedecision step and the scheduling step. Note that ifγ < (n +1) × l, it is not meaningful to outputl as the diversity constraintto the scheduling step, sincel-diversity can never be satisfied.Fortunately, in either case of Theorem 1, the value ofγ reflectsthe minimum total diversity we can satisfy for current news feedquery. To this end, we outputγ as the new diversity constraintto the scheduling step, in which we aim at maximizing the totalrelevance ofn+ 1 news feeds under that diversity constraint.

6 l-DIVERSITY CONSTRAINED NEWS FEED

SCHEDULING

The scheduling step receives the minimum total diversity (γ) fromthe decision step. In this section, we redefine the requirement O1of the l-Diversity Constrained Scheduling (DCS) Problem (seeDefinition 3) as: (O1’) messages inn + 1 news feeds fulfill theminimum total diversityγ. In the DCS problem with the redefinedrequirement, our objective is to compute a set ofn+1 news feedsthat satisfyγ and have the maximum total relevance score. Similarto the DCC problem, a brute-force method is very costly for theDCS problem. To this end, in this section we propose a three-stageheuristic algorithm to solve the DCS problem, and then analyzethe quality of its scheduled news feeds.

8

6.1 A Three-Stage Heuristic Algorithm

In this section, we solve the DCS Problem with a three-stageheuristic algorithm. In the first two stages, we neglect the factorof display weight (see Equation 2), only aiming at selectingk × (n + 1) messages to maximize theunweightedsum of theirrelevance scores. In the third stage, we rank the selected messagesin each news feed according to their relevance score.

6.1.1 Stage One: Satisfying l-Diversity Constraint

In this stage, we want to selectγ messages forn+ 1 news feeds,such that in each news feed, there are at mostl messages asso-ciating with distinct categories. After selecting suchγ messages,we guarantee thatn + 1 news feeds satisfy the minimum totaldiversityγ (see Definition 2). Since we neglect the display weightof positions in this stage, we focus on maximizing the sum ofrelevance scores of targetγ messages. We define this stage as theγ-Selection Problem.

Definition 5. γ-Selection Problem: Givenn+1 sets of candidatemessages for u’s query regions att0, t1, t2, . . . , andtn, alongwith their category and relevance score to u, D-MobiFeed selectsγ messages forn+ 1 news feeds, such that (O1) each news feedcontains at mostl messages with distinct categories, and (O2) thesum of relevance scores of these messages is maximized.

Modeling. The maximum flow model in Section 5 cannot bedirectly used here since it does not consider the message’s rele-vance score. We translate theγ-Selection Problem into aminimumcost flow problem[6]. Consider the example in Figure 3, the flowgraph representation of theγ-Selection problem (Figure 6) is al-most the same as that of the RDCC Problem in Section 5.1, exceptthe following two differences: (i) Each edgee(vi, vj) ∈ E has notonly a capacityc(vi, vj) but also acostw(vi, vj) (the value inparentheses in Figure 6). For each edgee(cj ,mk) between nodesin Nc (assumecj is in (i + 1)-th group ofNc) and nodes inNm, we set its costw(cj ,mk) = 1 − relevanceScore(u,mk),whererelevanceScore(u,mk) is the relevance score ofmk to uat ti. The cost of all the other edges inE is 0. In our example,since the relevance score ofm1 to u at t0 is 0.58 (Table I inFigure 3b), the cost of edge connecting node ‘Restaurant’ (in thefirst group ofNc) andm1 ∈ Nm is 1− 0.58 = 0.42. (ii) For thebalanceof nodes and t (i.e., b(s) and b(t)), they are no longervariables. Instead, they are set with fixed value, i.e.,b(s) = γ andb(t) = −γ, whereγ is theminimum total diversityderived fromthe maximum flow problem in Section 5.1, andγ is set to7 in ourexample.

Given the above flow graph, the modeledminimum costflow problem is to assign an integerflow value x(vi, vj) ∈[0, c(vi, vj)] for each edgee(vi, vj) ∈ E such that for everynodev ∈ V the flow conservation property (Equation 3) holds,and the following objective function is minimized:

G(x) =∑

e(vi,vj)∈E

w(vi, vj)× x(vi, vj). (4)

After solving the minimum cost flow problem formulated above,for any edge (cj ,mk) with x(cj ,mk) = 1 wherecj is in (i+1)-th group ofNc, it means that D-MobiFeed assignsmk to the newsfeed foru’s query region atti.

Proof of correctness.According to the correctness proof inSection 5.2, this minimum cost flow model can selectγ messageswhich satisfy the requirementO1 of the γ-Selection Problem

m1 Restaurant 0.68

Message CategoryRelevancescore to u

m2 Restaurant 0.58

m5 Theater 0.53

m10 Museum 0.55news feedat t0

news feedat t1

m3 Restaurant 0.1

m4 Stadium 0.53

m8 Shopping 0.5news feedat t2

m1 Restaurant 0.68

Message CategoryRelevancescore to u

m2 Restaurant 0.58

m10 Museum 0.55

m5 Theater 0.53

m11 Museum 0.5

news feedat t0

news feedat t1

m4 Stadium 0.53

m8 Shopping 0.5

m9 Shopping 0.5

m3 Restaurant 0.1

news feedat t2

(a) (b)

Fig. 7: (a) The assignment results of news feeds att0, t1, andt2after Stage One. (b) The assignment results of news feeds att0,t1, andt2 after Stages Two and Three.

(Definition 5). Furthermore, in the assignment result, every edgee(cj ,mk) with x(cj ,mk) = 1 incurs costw(cj ,mk) = 1 −relevanceScore(u,mk), and there are exactlyγ such edges (deter-mined by the balance of source nodes in Figure 6). Therefore, wehave:

G(x) =∑

e(vi,vj)∈E

w(vi, vj)× x(vi, vj)

=∑

x(cj,mk)=1

w(cj ,mk)

=∑

x(cj,mk)=1

(1 − relevanceScore(u,mk))

= γ −∑

0≤i≤n

unweightedRelevanceScore(fi), (5)

where unweightedRelevanceScore(fi) is the sum of relevancescores for messages in a news feedfi, regardless of the displayweight. Since the modeled minimum cost flow problem aims tominimizeG(x), the selectedγ messages have the maximum sumof relevance scores (Equation 5), which satisfies the requirementO2 in Definition 5.

Solution. In the literature, there are several algorithms pro-posed to solve the minimum cost flow problem, including networksimplex method [32], cost scaling [21], minimum mean cycle can-celing [24], and successive shortest path algorithm (SSPA)[14].We employ the SSPA algorithm, which is the most general ap-proach with the lowest complexityO(γ ·(|E|+|V |· log|V |)) [36],whereγ is the minimum total diversity in our scenario.

In our example, after solving the minimum cost flow prob-lem using the SSPA algorithm,{m2,m5,m10}, {m1} and{m3,m4,m8} are assigned to the news feeds att0, t1, and t2,respectively (Figure 7a).

6.1.2 Stage Two: Scheduling Remaining Messages

In Stage One, we have scheduledγ messages satisfying theminimum total diversity (γ). However, some news feeds may notbe full, and some candidate messages remain unscheduled. Inourexample, we can schedule one more message for the news feed att0 after Stage One (Figure 7a). Therefore, in this stage, we selectmessages from remaining candidate messages, such that eachofn + 1 news feeds accommodates (at most)k messages. Keepingthe objective of the DCS Problem (Definition 3) in mind, we alsomaximize the sum of relevance scores of newly selected messagesin this stage.

9

s

r0

r1 t

m7

m9

m11

m6

r2

1 (0)

1 (wjk)

1 (0)

b = 4 b = -43 (0)

1 (0)

1 (0)

1 (0)

1 (0)

Fig. 8: Flow graph representation of the Replenish-Up-To-k prob-lem.

Definition 6. Replenish-Up-To-k Problem: Given the results ofthe γ-Selection Problem, D-MobiFeed selects messages from re-maining candidate messages sets and adds them ton + 1 newsfeeds, such that (O1) in each news feed, there are at most kmessages, and (O2) the sum of relevance scores of newly selectedmessages is maximized.

Modeling. We also translate theReplenish-Up-To-k Probleminto a minimum cost flow problem. For our running example, itsflow graph representation is shown in Figure 8. Compared to therepresentation of theγ-Selection Problem (Figure 6), the flowgraph does not include the node setNc (i.e., categories) any more.Also,Nm only contains remaining candidate messages after StageOne. In our example, according to the assignment results afterStage One (Figure 7a), there are four messagesm6, m7, m9, andm11 can still be selected fromNm. In the flow graph the edgesetE consists of three types of edges: (i) An edgee(s, ri) forevery news feedri ∈ Nr has cost0 and capacityri.free, whereri.free indicates the number of unoccupied positions for the newsfeedri after performing the message assignment in Stage One. Inour example,r0.free = 1, r1.free = 3, andr2.free = 1. (ii) Anedgee(ri,mk) for every pair ofri ∈ Nr andmk ∈ Nm hascapacity1. Its costw(ri,mk) = 1 − relevanceScore(u,mk),where relevanceScore(u,mk) is the relevance score ofmk tou at ti. If mk 6∈ CandidateMsgi, i.e., mk is not the candidatemessage atti, we set relevanceScore(u,mk) = 0 (i.e., thedashed edges in Figure 8). (iii) An edgee(mk, t) for everymk ∈ Nm has cost0 and capacity1. Finally, we set thebalancesb(s) = γ′ and b(t) = −γ′, where the requiredflow γ′ equals min{|Nm|,

∑ri∈Nr

ri.free}. In our example,γ′ = min{4, 5} = 4. Thebalancesof other nodes are still set to0.

The same as the definition of theminimum cost flow problemdescribed in Section 6.1.1, our task is to assign an integerflowvalue x(vi, vj) ∈ [0, c(vi, vj)] for each edgee(vi, vj) ∈ E,such that for every nodev ∈ V the flow conservation property(Equation 3) holds, and the objective function (Equation 4)isminimized.

The Replenish-Up-To-k Problem is addressed by solving theminimum cost flow problem formulated above. Given the resultsof the flow value, for any pair (ri,mk) with x(ri,mk) = 1 andw(ri,mk) < 1 (i.e., mk ∈ CandidateMsgi), it means that D-MobiFeed addsmk to the news feed foru’s query region atti.

Proof of correctness.Since we set the capacity for each edgee(s, ri) as the number of unoccupied positions in news feedriafter Stage One, the requirementO1 is guaranteed. Moreover,similar to Equation 5, the sum of relevance score for each message

selected in this stage is negative linear to the total cost oftheresult flow. Therefore, the selected messages have maximum sumof relevance scores, which satisfies the requirementO2.

Solution. As in Section 6.1.1, we also employ the SSPAalgorithm to solve the minimum cost flow problem. In our example(Figure 8),m11 andm9 are added to the news feeds att0 andt2,respectively.

6.1.3 Stage Three: SortingAfter performing the first two stages, we have scheduled a setofmessages for each news feed. In this stage we consider the displayweight of different positions in the news feed. Intuitively, wedisplay a message with higher relevance score in a higher position(i.e., with a larger display weight). Therefore, for each ofn + 1news feeds, D-MobiFeed sorts the messages by their relevancescores in non-increasing order as its final result. Figure 7bdepictsthe final results of three news feeds for our running example.

6.2 Scheduling Quality Analysis

In this section we analyze the scheduling quality of the three-stage heuristic algorithm. After applying the three-stageheuristicalgorithm to solve the DCS Problem, news feedsf0, f1, . . . , andfn are generated, which have the property:

Theorem 2. The n + 1 news feeds generated bythe three-stage heuristic algorithm have the maximum∑

0≤i≤n unweightedRelevanceScore(fi) among all possiblescheduling schemes satisfying the minimum total diversityγ.

Proof. Suppose one unchosen messagem′ from candidatemessages for new feedfi (0 ≤ i ≤ n) can replaceone scheduled messagem ∈ fi, so we could increaseunweightedRelevanceScore(fi)

2 under the condition that thesen + 1 news feeds still satisfy the minimum total diversityγ. Ob-viously we haverelevanceScore(u,m) < relevanceScore(u,m′).

According to the description of the three-stage heuristic al-gorithm in Section 6.1, we can divide messages infi (beforereplacement) into two sets, i.e.,MD andMR, whereMD containsthe messages scheduled in the Stage One andMR stands forthe messages assigned in the Stage Two. (1) Ifm ∈ MR, afterreplacingm with m′ we increase the sum of relevance scoresfor messages inMR, Which is a contradiction according to thedefinition ofMR (see Definition 6). (2) Ifm ∈ MD, there are twocases. Assume that infi (before replacement), the set of categoriesfor messages belonging toMD is CD ; besides, messagem andm′ are associated with categorycm andcm′ , respectively. (a) Inthe first case,cm′ 6∈ CD − {cm}, which means after replacingmwith m′, n+1 news feeds still satisfy the minimum total diversityγ. Thus, we increase the sum of relevance scores for messages inMD, leading to a contradiction according to Definition 5. (b) Inthe second case,cm′ ∈ CD − {cm}. In order to guarantee thatn+ 1 news feeds still satisfy the minimum total diversityγ afterreplacement, there must be another scheduled messagem′′ ∈ MR

with its categorycm′′ 6∈ CD−{cm}. Sincem′′ belongs toMR in-stead ofMD in the originalfi, we haverelevanceScore(u,m′′) <relevanceScore(u,m) < relevanceScore(u,m′), i.e.,m′ is betterthanm′′. It contradicts with the fact that for the originalfi, thethree-stage heuristic algorithm schedulesm′′ instead ofm′ inMR.

2. I.e., the sum of relevance scores for messages in a news feed fi, regardlessof the display weight.

10

7 EXPERIMENT RESULTS

In this section, we first present experimental setting, and thenevaluate the performance of D-MobiFeed through experiments.

Experiment settings. We implemented the experiments inC++ using a real location-aware social network data set in NewYork City (NYC), USA, which was crawled from Foursquare [20]from December 15 to 25, 2012. The data set contains 417,898 geo-tagged messages (belong to 420 categories in total3) and 99,292users. We extracted the road map of NYC from USA CensusTIGER/Line Shapefiles [1] and randomly generated 1,000 30-minute trajectories using A* algorithm [25]. Unless mentionedotherwise, all users move with a constant speed of 40km/h, thelook-ahead steps (n) is 5, the minimum number of messagecategories per news feed (l) is 3, the minimum message displaytime (td) is 10 seconds, the number of messages per news feed(k) is 5, and the query range distance (D) is 600 meters. Basedon our experimental results, the average number of messagesina candidate message set is 109. All experiments were run on aUbuntu 11.10 machine with a 3.4GHz Intel Core i7 processor and16GB RAM.

Evaluated algorithms. In this section, we compare D-MobiFeed with two baseline approaches.

• n-LA-no-diversity: This algorithm is our previouswork [39] (i.e., MobiFeed).n-LA-no-diversity does NOTconsider any diversity in news feeds. Specifically, it looksaheadn steps and schedules messages amongn+ 1 newsfeeds using a greedy manner (i.e., a higher priority is givento a message with a larger relevance value computed byEquation 2).

• zero-LA: This algorithm is based on our D-MobiFeed, butits look-ahead step (n) is set to zero. In other words,zero-LA generates news feeds considering both diversity andrelevance, but it does not perform any location predictionand processes a news feed request at a time. This baselineis designed to evaluate the effectiveness of the look-aheadtechnique used by D-MobiFeed.

• n-LA: This is our proposed D-MobiFeed with the look-ahead technique (i.e.,n > 0).

Performance metrics.We evaluate the performance of evalu-ated algorithms in terms of three performance metrics.

• The number of categories:This metric indicates the qualityof news feeds, as it measures the average number ofcategories in a news feed.

• Relevance score:This metric shows the quality of newsfeeds by measuring the average total relevance score of anews feed.

• Running time:This metric indicates the efficiency of anevaluated algorithm. The total running time is split intothree parts, namely, scheduling step, decision step, andcandidate message step.

7.1 The Summary of Experimental Results

In this section, we first summarize the key findings in our experi-mental results.

Efficiency. Our proposed three-stage heuristic scheduling al-gorithm performs much better than the brute-force optimal al-gorithm by at least an order of magnitude in terms of running

3. In Foursquare, we define the category of a message as theprimarycategoryof its associated venue.

time (Figure 9b). Our D-MobiFeed with then-look-ahead method(n > 0) (i.e., n-LA) is more efficient than D-MobiFeed with thezero-look-ahead method (n = 0) (i.e., zero-LA) with respectto various levels of diversity requirements,n look-ahead steps,requested numbers of messages in a news feed, and query distanceranges, as depicted in Figures 10c, 11c, 12c, and 13c, respectively.This is because then-look-ahead method can effectively shareexecution among multiple news feeds simultaneously.

Diversity. n-LA outperforms our previous workn-LA-no-diversity (i.e., MobiFeed) in terms of diversity. In particular,n-LA-no-diversity cannot satisfy the defaultl-diversity requirement(l = 3) in all the experiments, whilen-LA can always satisfy thedefault value ofl (l = 3) and the required value ofl (up to l = 7in Figure 10a), as depicted in Figures 10a to 13a.

Relevance.Sincen-LA considers both relevance and diversity,it slightly reduces the relevance of news feeds compared to then-LA-no-diversity (i.e., MobiFeed), as depicted in Figures 10bto 13b. However, then-look-ahead method (n > 0) effectivelyimproves the relevance of news feeds compared tozero-LA(Figures 10b to 13b).

7.2 Comparison with the Optimal Solution

In this subsection, we mathematically formulate the DCS Problemin the scheduling step as an Integer Linear Programming (ILP)problem, which aids in better understanding of the problem.Also,we obtain the optimal solution using an ILP solver [27] andcompare it with our three-stage heuristic algorithm.

ILP formulation of DCS problem. Without loss of generality,given a news feed query with a look-ahead stepsn, we assume thatall n + 1 news feeds could satisfy thel-diversity constraint. Forthis query, there areNm distinctcandidate messages belonging toNc categories, as well asNp positions in the news feed result lists,whereNp = k×(n+1). We first define anNp×Nm matrixX asboolean variables to indicate the scheduling results. Specifically,each variablexij = 1 means that we assign a candidate messagemj to positionpi, wherei = k × a + b, andpi stands for theb-th position in the news feed result list atta; xij = 0 otherwise.Moreover, we have anNp × Nm weight matrixW , where eachelementwij indicates the score we could obtain for schedulingmj

to positionpi, i.e., relevanceScore(u,mj)× displayWeight(b, k).We also have anNm×Nc category matrixZ, where each elementzjh = 1 if mj belongs to categorych andzjh = 0 otherwise. TheILP formulation can be written as:

Maximize

Np∑

i=1

Nm∑

j=1

xij × wij , (6)

Subject to:xij = {0, 1} for all i, j, (7)

Nm∑

j=1

xij ≤ 1 for all i, (8)

Np∑

i=1

xij ≤ 1 for all j, and (9)

non zero element(EvXZ) ≥ l for all v. (10)

Constraints 7-9 guarantee that each position accommodatesatmost one message and each message could be assigned for atmost once. Constraint 10 corresponds to thel-diversity constraint.Specifically,Ev (0 ≤ v ≤ n) is anNp-dimension row vector,where the(v · k + 1)-th to (v · k + k)-th elements are set to

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one and others are set to zero. Each element ofEvX indicateswhether the corresponding message is scheduled in the news feedat tv . By multiplying EvX with Z we get anNc-dimensionrow vectorEvXZ, where each element shows whether the newsfeed at tv contains the corresponding category. The functionnon zero elementcounts the number of non-zero elements inEvXZ, which is the number of categories in the news feed attv.Constraint 10 is non-linear, but it can be reformulated as multiplelinear constraints by using an auxiliary vector variable [13]. Thus,all Constraints 7-10 become linear and in the standard ILP form.

Results.We use an ILP solver to get the optimal solution, andcompare it with our three-stage heuristic algorithm, as depicted inFig. 9. In this experiment, we calculate the average relative errorof our scheme by:Relative Error= 1

N× OptimalScore−HeuristicScore

OptimalScore ,whereN is the number of news feeds,OptimalScoreandHeuris-ticScoreare the total relevance scores of the news feeds computedby the optimal solution and our heuristic algorithm, respectively.Since the optimal solution is computationally expensive, we setthe look-ahead steps as two and vary the size of data set from20% to 100%. Fig. 9a shows that then-LA is very close to theoptimal solution (less than 1% error) in terms of relevance score.Furthermore,n-LA generates news feeds with higher score thanzero-LA (will be further described in Section 7.4). To comparethe efficiency of the optimal solution and three-stage heuristic al-gorithm, we show the running time of scheduling step (Section 4)in Fig. 9b. Here, ‘Z’, ‘N’, ‘O’ refer to zero-LA, n-LA, and theoptimal solution, respectively. The figure shows that our heuristicalgorithm is much more efficient and scalable than the optimalsolution.

Since the optimal solution cannot scale up to a large numberof messages, we will not test it in other experiments. Next wewill evaluate the performance of D-MobiFeed by varying differentparameters. To show the benefit of look-ahead technique in D-MobiFeed equipped withn-LA, we employ thezero-LA as abaseline approach. Moreover, to show the loss of relevance for thesake of diversity in D-MobiFeed, we implemented the schedul-ing algorithm in MobiFeed [39] (termedn-LA-no-diversity) asanother baseline.n-LA-no-diversity does not consider diversityof news feeds. It looks aheadn steps and schedules messagesamongn+ 1 news feeds in a greedy manner (i.e., giving a higherpriority to a message with a larger value computed by Equation 2in Section 4).

7.3 Effect of the l-diversity Constraints

Fig. 10 depicts the performance ofn-LA and the two baselinealgorithms with respect to the increase of the minimum numberof message categories per news feed (i.e.,l) from 1 to 10. Inthis experiment we setk = 10 to guarantee thatk ≥ l. The

performance ofn-LA-no-diversity is not affected by the value ofl. Fig. 10a shows thatn-LA-no-diversity generates news feedswith only roughly two categories, whilen-LA provides morediverse news feeds with largerl (Fig. 10a). Thus, D-MobiFeedprovides more satisfactory news feeds compared to MobiFeed.Although n-LA generates news feeds with the best diversity,some of its news feeds may not be able to satisfy thel-diversityconstraint, as we discussed in Section 5; and thus, the averagenumber of categories per news feed could be smaller thanl.zero-LA performs worse thann-LA because it only tries to finddiverse messages for a single news feed. However,n-LA schedulesmessages with different categories among multiple news feeds,so it has a chance to balance between the diversity and therelevance of news feeds (Fig. 10b). Fig. 10c depicts thatn-LA-no-diversity (abbreviated as ‘D’) is the most efficient due to itsgreedy characteristic [39]. The running time of ourn-LA increasesas l gets larger. This is because, in the Stage One of our three-stage heuristic algorithm in the scheduling step, the valueof γgets larger with the increase ofl, thus increasing the complexityof the SSPA algorithm (see Section 6.1.1). D-MobiFeed is scalablewith the increase of valuel. Furthermore,zero-LA incurs thelargest computational overhead, since it has to perform decisionand scheduling steps more times thann-LA.

7.4 Effect of Look-ahead Steps

In this experiment, we evaluate the effect of look-ahead steps (i.e.,n, varying from 1 to 10, on the performance of D-MobiFeed. Asdepicted in Fig. 11a, although the average number of categoriesper news feed of bothn-LA andn-LA-no-diversity is less than thedefault value ofl = 3, n-LA doubles the number of categories pernews feed as inn-LA-no-diversity. Besides, whenn gets larger,n-LA could generate news feeds with more categories. The mainreason is that, by looking ahead more steps,n-LA has a higherchance to assign a message with a certain category to a betternewsfeed within its lifetime, such that the diversity constraint could besatisfied to a larger extent. Fig. 11b shows that, compared ton-LA-no-diversity, there is a slight loss (i.g., less than 3%) of relevancefor ourn-LA. Asn gets larger, the improvement of generated newsfeeds’ relevance forn-LA is larger than that ofzero-LA (Fig. 11b),since more query regions are considered at one time, thus makinga message scheduled to a better news feed to maximize the totalrelevance score. In terms of the efficiency, whenn becomes larger,the running time ofn-LA initially decreases (Fig. 11c). However,after n is larger than five, its running time increases slightly.The main reason is that, whenn is small, n-LA benefits fromsharing the computation of schedulingn + 1 news feeds for auser’s location update; asn gets larger, this benefit is offset by theincrease of overhead for our three-stage heuristic algorithm in thescheduling step, since there are more candidate messages withinn + 1 query regions, leading to more computation time spent ona flow graph with more nodes. D-MobiFeed efficiently providesnews feeds with higher levels of diversity while preservingtheirhigh quality in terms of relevance.

7.5 Effect of News Feed Size

This experiment investigates the effect of user-requestednews feedsize (i.e.,k) on the performance of all the algorithms by increasingk from 3 to 10. The value ofk starts from 3 because we needto ensure thatk is equal to or larger than the defaultl-diversity

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constraint (i.e.,l = 3). Fig. 12a shows that, on the one hand,n-LA-no-diversity cannot generate news feeds with more than twocategories even if we increase the value ofk to 10; on the otherhand, D-MobiFeed could generate news feeds whose number ofcategories is close to the required diversity constraint (i.e., l =3). The reason is that, the Stage One of our three-stage heuristicalgorithm generates news feeds with the largest extent of diversity.It is also expected that the number of categories in a news feedincreases whenk gets larger (Fig. 12a). Fig. 12b depicts that the

loss of relevance for our scheme compared ton-LA-no-diversityis minor. Furthermore, the increase ofk leads to more messagesin a news feed, so the total relevance score of news feed getshigher. However, whenk gets larger, we need to replenish moremessages in the Stage Two of our three-stage heuristic algorithm,so its running time gets longer (Fig. 12c).

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7.6 Effect of Query Range Distance

This experiment studies the effect of user-specified query rangedistance (i.e.,D) on the performance of all the algorithms withvariousD from 200 to 1,000 meters, as shown is Fig. 13. It isexpected that largerD leads to more candidate messages for aquery region. Thus, all the algorithms find more diverse newsfeeds(Fig. 13a) and more relevant news feeds (Fig. 13b). However,Fig. 13c shows that the running time of all the algorithms getslarger whenD increases, as they need to retrieve more candidatemessages and process them to generate news feeds.

7.7 Effect of Minimum Display Time

Fig. 14 depicts the performance ofzero-LA, n-LA, andn-LA-no-diversity with respect to the increase of the minimum display time(i.e., td) from 5 to 30 seconds. Fig. 14a shows that, compared ton-LA-no-diversity, n-LA provides messages associated with morecategories due to the diversity constraint. Furthermore, as td getslarger, there are more categories in each news feed. The mainreason is that, the overlapping area between two consecutive queryregions becomes smaller whentd increases, so there are moredistinct candidate messages (thus belonging to more categories)in each query region. As a result, there is a higher chance forourscheduler to generate more diverse news feeds. When we havemore distinct candidate messages in each query region with largertd, our news feed scheduler has a higher chance to generate newsfeeds with better relevance (Fig. 14b). In general, D-MobiFeedprovides a better trade-off between the diversity and relevance ofmessages compared to MobiFeed. However,td should not be toolarge because mobile users may miss nearby relevant messages.The efficiency of all the algorithms becomes worse whentd getslarger, since the scheduler has to process more distinct messages(Fig. 14c).

7.8 Effect of Location Prediction Errors

This section evaluates the effect of errors of the location predictionfunction (Section 3.2.1). We randomly generate 10,000 trajectorieson the road map with speeds randomly selected from 20km/h tousers’ maximum movement speed (40 km/h by default). 5,000trajectories are randomly selected as a training set for thelocationprediction function. We use the remaining 5,000 trajectories as atest set to evaluate the effect of the location prediction algorithm.In the experiments, a prediction error occurs if the differencebetween a user’s actual location and predicted location is largerthan the tolerance thresholdθ that is set to 50 meters [15]. Whena prediction error takes place, the scheduler needs to re-schedulenews feeds based on a user’s location update. We measure the

TABLE 1: Prediction error (look-ahead steps).n 1 2 3 4 5 6 7 8 9 10

Error (%) 1.4 14.7 16.9 18.6 19.4 20.0 21.121.3 21.4 21.5

prediction error as the ratio of the number of prediction errors tothe number of location predictions.

Fig. 15 and Table 1 depict the experimental results with anincrease of the look-ahead steps (n) from 1 to 10. Fig. 15a and bexhibit the similar trend of diversity and relevance compared totheir counterparts without prediction errors, as depictedin Fig. 11aand b, respectively. Fig. 15c shows that, a largern increases therunning times of our schedulers with errors in location predictionfunction. This is because asn gets larger, D-MobiFeed needs topredict longer path, and there is a higher chance for a predictionerror to occur (Table 1). When more prediction errors take place,the scheduler has to re-schedule more news feeds based on updatedlocations, thus incurring higher computational overhead.

8 CONCLUSION

In this paper, we design D-MobiFeed; a location-aware news feedframework takes the relevance and diversity of news feeds into ac-count when scheduling news feeds for moving users. D-MobiFeedusers can specify the minimum number of categories in a newsfeed as anl-diversity constraint, and it aims at maximizing the totalrelevance of generated news feeds and satisfying thel-diversityconstraint. We focus on two key problems in D-MobiFeed, namely,decision and optimization problems. For the decision problem, wemodel it as a maximum flow problem and enable D-MobiFeed todecide whether it can fulfill thel-diversity constraint for a newsfeed. For the optimization problem, we design an efficient three-stage heuristic algorithm to maximize the total relevance of newsfeeds under thel-diversity constraint. We evaluate the performanceof D-MobiFeed using a real social network data set crawled fromFoursquare and a real road network. Experimental results showthat D-MobiFeed can efficiently provide location- and diversity-aware news feeds when maintaining their high quality in terms ofrelevance.

Our future direction is to measure the dissimilarity of pair-wise messages in terms of their category information and studya new multi-objective optimization problem of finding a set ofnews feeds, in which each news feed satisfies thel-diversityconstraint and the dissimilarity of the messages in each news feedis maximized while maximizing the total relevance of a set ofn+1news feeds for mobile users (wheren is the look-ahead step).

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Wenjian Xu received the bachelor’s degree insoftware engineering from Northwestern Poly-technical University, Xi’an, China, in 2010. He ispursuing his M.Phil. degree at the City Universityof Hong Kong. His research interests span queryprocessing, query optimization and big data an-alytics.

Chi-Yin Chow received the M.S. and Ph.D.degrees from the University of Minnesota-TwinCities in 2008 and 2010, respectively. He iscurrently an assistant professor in Departmentof Computer Science, City University of HongKong. His research interests include spatio-temporal data management and analysis, GIS,mobile computing, and location-based services.He is the co-founder and co-organizer of ACMSIGSPATIAL MobiGIS 2012, 2013, and 2014.