Heuristics for k-domination models of facility location problems in street networks

TL;DR

This paper introduces new greedy and beam search heuristics for finding small k-dominating sets in street network graphs, improving over existing methods especially for larger k values.

Contribution

The paper proposes novel heuristic algorithms inspired by a new problem formulation, demonstrating their effectiveness on street network graphs for k-domination problems.

Findings

New heuristics outperform benchmarks for k>1

Performance gain increases with larger k

Methods perform similarly for 1-domination case

Abstract

We present new greedy and beam search heuristic methods to find small-size $k$-dominating sets in graphs. The methods are inspired by a new problem formulation which explicitly highlights a certain structure of the problem. An empirical evaluation of the new methods is done with respect to two existing methods, using instances of graphs corresponding to street networks. The k-domination problem with respect to this class of graphs can be used to model real-world facility location problem scenarios. For the classic minimum dominating set ($1$-domination) problem, all except one methods perform similarly, which is due to their equivalence in this particular case. However, for the k-domination problem with k>1, the new methods outperform the benchmark methods, and the performance gain is more significant for larger values of k.