Finding the Sites with Best Accessibilities to Amenities

Qianlu Lin, Chuan Xiao, Muhammad Aamir Cheema and Wei Wang

University of New South Wales, Australia

Application

Find an apartment that is closest to restaurant, bus stop and zoo

‘Closeness’ is measured by a monotonic scoring function

Apartment

Restaurant

Bus Stop

Zoo

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Problem Definition

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•Given a set of query points S = {s1, s2, … sm}

•Given n sets of data points T1, T2, … Tn

•Find k query points in S, whose aggregated distances to T1, T2, … Tn are smallest:

Distance(sj, {T1, T2, … Tn})

= f(d(sj, NN(sj, T1)), d(sj, NN(s

j, T2)), … d(sj, NN(s

j, Tn)))

where NN(sj, Ti) is the nearest neighbour of sj in Ti

d(sj, NN(sj, Ti) is the distance from sj to its nearest neighbour in Ti

* For simplicity, we use:

d(x, y) is Euclidean Distance

f(x1, x2, ...xm) =sum(x1, x2, …, xm)

Related Literature

KNN – K Nearest Neighbour Given a query point q and a set of data points I, find k

data points in I that are nearest neighbour of q

RNN – Reverse Nearest Neighbour Given a query point q and a set of data points I, find k

data points of which q is the nearest neighbour

ANN – All Nearest Neighbour Given a set of query points Q and a set of data points I,

find nearest neighbour in I for each query point in Q (Y.Chen, ICDE2007) Efficient evaluation of all-nearest-

neighbor queries In solving our problem, we can retrieve ANN in each type

and find top k queries

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Our Contribution

We introduced the problem of finding the sites with best accessibilities to amenities

We proposed two algorithms to find top-k accessible sites among a set of possible locations

We performed experiments on several real datasets

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Baseline

Apartment

Restaurant

Bus Stop

Zoo

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ANN is used to retrieve the nearest neighbour of each query for each type.

Baseline - Disadvantage

I/O time Query data will be accessed n times, n is the

number of types of index objects

Memory usage Need find NN for all the query points Need to maintain a list of nearest neighbours

of each type of each query

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Separate Tree (Index Construction)

Apartment

Restaurant

Bus Stop

Zoo

Q1

Q2 Q3 Q4Z1

Query Tree

Index Tree

Z1

R1

R2

R3

R4

R1

R2 R3 R4

R1B1

B2

B3

B4

B1

B2 B3 B4

Q1Q2

Q4Q3

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Separate Tree (Query Processing)

Q1

Q1 Z1R1B1

MAXD={30, 305, 309}

MIND={30, 0, 0} LBD=30

UBD=644

current_k_best = 644

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R1 B1

Apartment

Restaurant

Bus Stop

Zoo

Z1

Z1

R1R1B1

Q1Q2

Q4Q3 MAXDMaximum distance from Q1 to all the nodes in the list

MINDMinimum distance from Q1 to all the nodes in the list

UBDUpper bound of the summed distance

LBDLower bound of the summed distance

Separate Tree (cont’d)

current_k_best = 190

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Apartment

Restaurant

Bus Stop

Zoo

Z1

R1

R2

R3

R4

R1B1

B2

B3

B4

Q1Q2

Q4Q3

Z1 R1

R2 R3 R4

B1

B2 B3 B4

Q1

Q2 Q3 Q4

Q3 Z1R4B2

MAXD={30, 100, 60}MIND={30, 0, 0} LBD=30

UBD=190

R3

Q4 Z1R4B3

MAXD={300, 150, 60}

MIND={300, 60, 30}

B4

LBD=360

UBD=510

More Improvement?

Data points from different type can be put into one bounding box

– To reduce I/O cost

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One Tree (Index Construction)

Apartment

Restaurant

Bus Stop

Zoo

I1

I2 I6

I3

I4

I5

I1

I2 I3 I4 I5 I6

Q1

Q2 Q3 Q4

I17

I17I18

I12

I9

I10

I11

I12I11 I7 I8 I13 I14 I15 I16 I9 I10 I18

I16I15

I8

I14I13

I7Query Tree

Index Tree

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Q1Q2

Q4Q3

Each node has a bitmap that indicates what types are contained in the node

One Tree (Query Processing)

Apartment

Restaurant

Bus Stop

Zoo

Q1

I1

I1 Q1

Q1 I1

MAXD={309, 309, 309}

MIND={0, 0, 0}

LBD=0

UBD=309*3=927

current_k_best = 972

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One Tree (cont’d)

Apartment

Restaurant

Bus Stop

Zoo

Q1 Q2

Q3 Q4

I1

I2 I6

I3

I4

I5

I1

I2 I3 I4 I5 I6

Q1

Q2 Q3 Q4

Q3 I4 I5

Q4 I6 I5

MIND={0, 0, 30} MAXD={50, 50, 30}LBD=30 UBD=130

MIND={30, 30, 140} MAXD={50, 50, 140}LBD=100 UBD=240

current_k_best = 130

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Experiments

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DataSet:San Francisco Road Network (SF) & Road Network of

North America (NA)Spatial query dataset, 2 dimensionsIndex: ~174k points (totally)Query: ~17k points

Algorithm:BaselineSeparate TreeOne Tree

Measurement:CPU timeNumber of leaf nodes access (I/O time)

Results (CPU Time VS. k)

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Results (CPU Time VS. |T|)

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Results (Leaf Node No. VS. k)

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Results (Leaf Node No. VS. |T|)

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Conclusion

We proposed two algorithms:Separate tree: creates indexes for different

types of points in separate R-treesOne tree: indexes all the points in a single R-

tree Both algorithms outperform the baseline

algorithm with a speed-up up to 5.7 times Also, both algorithms only need access the Query

tree once, which reduces I/O cost on accessing Query tree

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Thank you!

Questions?