Reverse Nearest Neighbor Heat Maps: A Tool for Influence Exploration

TL;DR

This paper introduces a novel algorithm called CREST for efficiently constructing reverse nearest neighbor heat maps, which visualize influence distribution in 2D space, supporting applications like marketing and resource management.

Contribution

The paper formulates the Region Coloring problem for RNN heat maps and proposes CREST, an asymptotically optimal algorithm that significantly improves efficiency over existing methods.

Findings

CREST outperforms alternative algorithms by several orders of magnitude.

CREST is proven to be asymptotically optimal in the worst case.

Extensive experiments validate CREST's efficiency on real and synthetic datasets.

Abstract

We study the problem of constructing a reverse nearest neighbor (RNN) heat map by finding the RNN set of every point in a two-dimensional space. Based on the RNN set of a point, we obtain a quantitative influence (i.e., heat) for the point. The heat map provides a global view on the influence distribution in the space, and hence supports exploratory analyses in many applications such as marketing and resource management. To construct such a heat map, we first reduce it to a problem called Region Coloring (RC), which divides the space into disjoint regions within which all the points have the same RNN set. We then propose a novel algorithm named CREST that efficiently solves the RC problem by labeling each region with the heat value of its containing points. In CREST, we propose innovative techniques to avoid processing expensive RNN queries and greatly reduce the number of region labeling operations. We perform detailed analyses on the complexity of CREST and lower bounds of the RC problem, and prove that CREST is asymptotically optimal in the worst case. Extensive experiments with both real and synthetic data sets demonstrate that CREST outperforms alternative algorithms by several orders of magnitude.