Reverse furthest neighbors in spatial databases
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Reverse Furthest Neighbors in Spatial Databases. Bin Yao , Feifei Li, Piyush Kumar Florida State University, USA. 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 :

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Reverse Furthest Neighbors in Spatial Databases

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Reverse Furthest Neighbors in Spatial Databases

Bin Yao, Feifei Li, Piyush Kumar

Florida State University, USA


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)


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.


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.


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.


BRFN Example

: customer

: product


MRFN and BRFN

  • MRFN for q and P:

  • BRFN for a point q in Q and P are:


Outline

  • MRFN

    • Progressive Furthest Cell Algorithm

    • Convex Hull Furthest Cell Algorithm

    • Dynamically updating to dataset

  • BRFN


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.


Progressive Furthest Cell Algorithm (PFC)PFC(Query q; R-tree T)

  • Update fvc(q) using points contained by entries in ;

  • Filter points in using fvc(q);

  • 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 ;


Outline

  • MRFN

    • Progressive Furthest Cell Algorithm

    • Convex Hull Furthest Cell Algorithm

    • Dynamically updating to dataset

  • BRFN


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.)

CHFC(Query q; R-tree T (on P))

// compute only once

  • 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;


Outline

  • MRFN

    • Progressive Furthest Cell Algorithm

    • Convex Hull Furthest Cell Algorithm

    • Dynamically updating to dataset

  • BRFN


Dynamically updating to dataset

  • PFC: update R-tree

  • CHFC:

    • update R-tree& re-compute CH (expensive)

    • Qhull algorithm


Dynamically Maintaining CH: insertion


Dynamically Maintaining CH: deletion

The qhull algorithm


Dynamically Maintaining CH

Adapt qhull to R-tree


Outline

  • MRFN

    • Progressive Furthest Cell Algorithm

    • Convex Hull Furthest Cell Algorithm

    • Dynamically updating to dataset

  • BRFN


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.


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;


BRFN: Disk-Resident Query Group

Limitation: query group size may not fit in memory

Solution: Approximate convex hull of Q (Dudley’s approximation)


Experiment Setup

  • Dataset:

    • Real dataset (Map: USA, CA, SF)

    • Synthetic dataset (UN, CB, R-Cluster)

  • Measurement

    • Computation time

    • Number of IOs

    • Average of 1000 queries


MRFN algorithm

CPU computation

Number of IOs


BRFN algorithms

CPU: vary A, Q=1000

IOs: vary A, Q=1000


Scalability of various algorithms

BRFN number of IOs

MRFN number of IOs


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.


Thank you!Questions?


Datasets: San Francisco


Datasets: California


Datasets: North America


Datasets : uncorrelated uniform


Datasets : correlated bivariate


Datasets : random clusters


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