Heuristics for Minimum Weight Directed Dominating Set Problem

For any node-weighted directed graph (digraph), a directed dominating set \(S_{D}\) is a subset of nodes such that every node of the digraph either belongs to \(S_{D}\) or has an arc directed from a node in \(S_{D}\) to itself. The minimum weight directed dominating set problem (MWDDS) seeks a directed dominating set with minimum sum of weights of its constituent nodes. It is an \(\mathcal {NP}\)-hard combinatorial optimization problem which finds applications in modelling a wide variety of directed interactions in complex heterogeneous networks like chemical reaction, metabolic regulation, spread of an infectious disease. In this paper, we present five greedy heuristics to solve MWDDS. To our knowledge, these are the first heuristic approaches for MWDDS. We have also proposed a local search based on redundant node removal to improve the solutions obtained by these greedy heuristics. Performance of these five heuristics were evaluated on a wide range of digraph instances. Computational results show the effectiveness of these heuristics.