Multispace, Dynamic, Fixed-Radius, All Nearest Neighbours Problem

We present a solution to a specific version of one of the most fundamental computer science problem - the nearest neighbour problem (NN). The new, proposed variant of the NN problem is the multispace, dynamic, fixed-radius, all nearest neighbours problem, where the NN data structure handles queries that concern different subsets of input dimensions. In other words, solutions to this problem allow searching for closest points in terms of different features. This is an important issue in the context of practical applications of incremental state abstraction techniques for high dimensional Markov Decision Processes (MDP). The proposed solution is a set of simple, one-dimensional structures, that can handle range queries for arbitrary subset of input dimensions for the Chebyshev distance. We also provide version for other metrics, and a simplified version of the algorithm that yields approximate results but runs faster. The proposed approximation is deterministic in a way that ensures that the most important (in the context of the considered state abstraction task) parts of the result are returned with no accuracy loss. The presented experimental study demonstrates improvement in comparison to some state-of-the-art algorithms on uniformly random and MDP-generated data.