Some Observations on Algorithms for Computing Minimum Independent Dominating Set

In this paper, we present some observations on the various algorithms proposed to find a Minimum Independent Dominating Set (MIDS). MIDS is proven to be an NP-hard problem. We compared an exact algorithm based on intelligent subset enumeration with another exact algorithm based on matching in graphs. We found that the former performs better than the latter for small graphs despite having a worse asymptotic complexity. There is only one Polynomial Time Approximation Scheme (PTAS) proposed in literature for computing MIDS which works for polynomially bounded growth graphs. We observed that changing the

ε

value in the PTAS reduces the running time quite drastically but does not increase the cardinality returned significantly. We compared the cardinality of the IDS returned by various heuristics for grid, unit disk graph and general graph topologies. The results show that the highest degree heuristic returns the best cardinality amongst all these algorithms in literature for all graphs except grid graphs for which the inter-dominator 3-hop distance heuristic performs better. To the best of our knowledge, this is the first empirical study where the exact, PTAS and heuristic solutions to the MIDS problem have been compared in terms of the quality of the solution returned as well as provide insights into the behavior of these approaches for various types of graphs.