reverse furthest neighbors in spatial databases
DESCRIPTION
Reverse Furthest Neighbors in Spatial Databases. Bin Yao , Feifei Li, Piyush Kumar Florida State University. A Novel Query Type. Reverse Furthest Neighbors (RFN) Given a point q and a data set P, find the set of points in P that take q as their furthest neighbor Two versions : - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/1.jpg)
Reverse Furthest Neighbors in Spatial Databases
Bin Yao, Feifei Li, Piyush Kumar
Florida State University
![Page 2: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/2.jpg)
A Novel Query Type Reverse Furthest Neighbors (RFN)
Given a point q and a data set P, find the set of points in P that take q as their furthest neighbor
Two versions: Monochromatic Reverse Furthest Neighbors (MRFN) Bichromatic Reverse Furthest Neighbors (BRFN)
![Page 3: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/3.jpg)
Motivation and Related works
Motivation: inspired by RNN Reverse Nearest Neighbor
Set of points taking query point as their NN.Monochromatic & Bichromatic RNN
Many applications that are behind the studies of the RNN have the corresponding “furthest” versions.
![Page 4: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/4.jpg)
MRFN Application P: a set of sites of interest in a region For any site, it could find the sites that take itself
as their furthest neighbors This has an implication that visitors to the RFN of
a site are unlikely to visit this site because of the long distance.
Ideally, it should put more efforts in advertising itself in those sites.
![Page 5: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/5.jpg)
BRFN Application P: a set of customers Q: a set of business competitors offering similar
products A distance measure reflecting the rating of
customer(p) to competitor(q)’s product. A larger distance indicates a lower preference. For any competitor in Q, an interesting query is to
discover the customers that dislike his product the most among all competing products in the market.
![Page 6: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/6.jpg)
BRFN Example : customer : product
876531 ,,,,: of RFN pppppq
1p
2p
1q
4p
3p
6p
5p8p
2q
3q
7p
4213 ,,: of RFN pppq : of RFN 2q
![Page 7: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/7.jpg)
MRFN and BRFN
MRFN for q and P:
BRFN for a point q in Q and P are:
q),fn(),,( QpPppPQqBRFN
q)}{,fn(),( qPpPppPqMRFN
![Page 8: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/8.jpg)
Outline
MRFNProgressive Furthest Cell AlgorithmConvex Hull Furthest Cell AlgorithmDynamically updating to dataset
BRFN
![Page 9: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/9.jpg)
MRFN: Progressive Furthest Cell Algorithm (first algorithm) Lemma: Any point from the furthest Voronoi cell(fvc) of p
takes p as its furthest neighbor among all points in P.
1p
3p2p
)( 1pfvc
5p4p
![Page 10: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/10.jpg)
Progressive Furthest Cell Algorithm (PFC)PFC(Query q; R-tree T)
Initialize two empty vectors and ; priority queue L with T’s root node; fvc(q)=S;
While L is not empty do Pop the head entry e of L If e is a point then, update the fvc(q)
If fvc(q) is empty, return; If e is in fvc(q), then Push e into ;
else If e fvc(q) is empty then push e to ; Else for every child u of node e
If u fvc(q) is empty, insert u into ; Else insert u into L ;
CV PV
CV
PV
PV Update fvc(q) using points contained by entries in ; Filter points in using fvc(q);CV
PV
1p
3p2p
)( 1pfvc
4p
)( 1pfvc
![Page 11: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/11.jpg)
Outline
MRFNProgressive Furthest Cell AlgorithmConvex Hull Furthest Cell AlgorithmDynamically updating to dataset
BRFN
![Page 12: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/12.jpg)
MRFN: Convex Hull Furthest Cell Algorithm(second algorithm)
Lemma: the furthest point for p from P is always a vertex of the convex hull of P. (i.e., only vertices of CH have RFN.)
Find the convex hull of P; if , then return empty; else
Compute using ; Set fvc(q,P*) equal to fvc(q, ); Execute a range query using fvc(q,P*) on T;
PC
PCq
*PC }{qCP
*PC
CHFC(Query q; R-tree T (on P))
// compute only once
![Page 13: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/13.jpg)
Outline
MRFNProgressive Furthest Cell AlgorithmConvex Hull Furthest Cell AlgorithmDynamically updating to dataset
BRFN
![Page 14: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/14.jpg)
Dynamically updating to dataset
PFC: update R-tree CHFC:
update R-tree& re-compute CH (expensive)Qhull algorithm
![Page 15: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/15.jpg)
Dynamically Maintaining CH: insertion
1p4p
3p2p
6p
5p
7p}{}{ 77 pCpP P
CC
![Page 16: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/16.jpg)
Dynamically Maintaining CH: deletion
2p
8p
1p9p
3p
4p5p
6p
7p
The qhull algorithm
![Page 17: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/17.jpg)
Dynamically Maintaining CH
2p
3p
2e
3e
1e
1p
minVdist
maxVdist
Adapt qhull to R-tree
![Page 18: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/18.jpg)
Outline
MRFNProgressive Furthest Cell AlgorithmConvex Hull Furthest Cell AlgorithmDynamically updating to dataset
BRFN
![Page 19: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/19.jpg)
BRFN
After resolving all the difficulties for the MRFN problem, solving the BRFN problem becomes almost immediate.
Observations: all points in P that are contained by fvc(q,Q) will have
q as their furthest neighbor. Only the vertexes of the convex hull have fvc.
![Page 20: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/20.jpg)
BRFN algorithm
BRFN(Query q, Q; R-tree T) Compute the convex hull of Q; If then return empty; Else
Compute fvc(q, );Execute a range query using fvc(q, ) on T;
QC
QCq
QC
QC
![Page 21: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/21.jpg)
BRFN: Disk-Resident Query Group
Limitation: query group size may not fit in memory
Solution: Approximate convex hull of Q (Dudley’s approximation)
![Page 22: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/22.jpg)
Experiment Setup
Dataset: Real dataset (Map: USA, CA, SF)Synthetic dataset (UN, CB, R-Cluster)
MeasurementComputation time Number of IOsAverage of 1000 queries
![Page 23: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/23.jpg)
MRFN algorithm
CPU computation Number of IOs
![Page 24: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/24.jpg)
BRFN algorithms
CPU: vary A, Q=1000 IOs: vary A, Q=1000
![Page 25: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/25.jpg)
Scalability of various algorithms
MRFN number of IOs BRFN number of IOs
![Page 26: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/26.jpg)
Conclusion
Introduced a novel query (RFN) for spatial databases.
Presented R-tree based algorithms for both versions of RFN that feature excellent pruning capability.
Conducted a comprehensive experimental evaluation.
![Page 27: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/27.jpg)
Thank you!Questions?
![Page 28: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/28.jpg)
Datasets: San Francisco
![Page 29: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/29.jpg)
Datasets: California
![Page 30: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/30.jpg)
Datasets: North America
![Page 31: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/31.jpg)
Datasets : uncorrelated uniform
![Page 32: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/32.jpg)
Datasets : correlated bivariate
![Page 33: Reverse Furthest Neighbors in Spatial Databases](https://reader036.vdocuments.net/reader036/viewer/2022062323/56815854550346895dc5b0cc/html5/thumbnails/33.jpg)
Datasets : random clusters