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The Reverse Nearest Neighbor (RNN) Query

The Reverse Nearest Neighbor (RNN) Query. Donghui Zhang CCIS Northeastern University. Reverse NN: Definition. Given a set of points, and a query location q. Find the points whose NN is q. RNN( q )={ p 1 , p 2 }, NN(q)= p 3. p. p. 4. 1. p. 3. q. p. 2. Half-plane pruning. p. p.

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The Reverse Nearest Neighbor (RNN) Query

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  1. The Reverse Nearest Neighbor (RNN) Query Donghui Zhang CCIS Northeastern University

  2. Reverse NN: Definition • Given a set of points, and a query location q. • Find the points whose NN is q. • RNN(q)={p1, p2}, NN(q)= p3. p p 4 1 p 3 q p 2

  3. Half-plane pruning p p 1 1 p 2 First NN N 1 First NN N 2 p' p ^ q ( ) , 1 ^ ( p , q ) p ^ q ( ) , q 2 q Second NN

  4. (TPL) Algorithm • Two logical steps: • Filter step: Find the set Scnd of candidate points • Find NN; • Prune space; • Find NN in unpruned space; • … • Till no more object left. • Refinement step: eliminate false positives • For each point p in Scnd, check whether its NN is not q. • The two steps are combined in a single tree traversal, by keeping all pruned MBRs/objects in Srfn.

  5. Example

  6. Example

  7. Example

  8. Example

  9. Example

  10. Example

  11. Example (end of filter step)

  12. Example (end of filter step)

  13. Example (refinement)

  14. Example (refinement)

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