Efficient Reverse k Nearest Neighbor evaluation for hierarchical index

TL;DR

This paper identifies flaws in existing algorithms for reverse k-nearest neighbor queries over hierarchical indexes, provides counterexamples, and proposes a corrected, validated algorithm to improve accuracy and reliability.

Contribution

The paper introduces a new correct algorithm for monochromatic RkNN queries over hierarchical indexes, addressing flaws in previous methods.

Findings

Previous algorithms had correctness flaws validated by counterexamples.

The proposed algorithm is correct under identified necessary conditions.

The new method improves reliability of RkNN query processing.

Abstract

"Reverse Nearest Neighbor" query finds applications in decision support systems, profile-based marketing, emergency services etc. In this paper, we point out a few flaws in the branch and bound algorithms proposed earlier for computing monochromatic RkNN queries over data points stored in hierarchical index. We give suitable counter examples to validate our claims and propose a correct algorithm for the corresponding problem. We show that our algorithm is correct by identifying necessary conditions behind correctness of algorithms for this problem.