Monochromatic RkNN queries in time-dependent road networks

Abstract

The problem of finding influence sets for a specific point, e.g. determining the influence of a location for a new restaurant on competitive restaurants, can be modeled as the reverse k nearest neighbor (RkNN) query. Although a lot of research has already been published on this topic, there is no adequate solution to solve the problem in time-dependent networks. In this work, we address RkNN queries in networks considering time-dependency, e.g. in road networks where traffic conditions influence the travel speed. Due to that the reverse nearest neighbors set can change over time, even if the objects are assumed to be static. We present an algorithm that solves the monochromatic time-dependent RkNN problem efficiently for a specific point in time. This algorithm uses a pruning technique to minimize the necessary network expansion. Furthermore, we present a variant of the algorithm which uses apriori knowledge from a pre-processing step to save further network expansion. Finally, we compare the proposed methods for monochromatic queries to a simple baseline approach by using time-dependent road networks of different sizes, various densities for the points of interests and various values for k. The results show that our proposed algorithms are orders of magnitude faster than a straightforward alternative.