Improved approximations of independent dominating set in bounded degree graphs

Abstract

We consider the problem of finding an independent dominating set of minimum cardinality in bounded degree and regular graphs. We first give approximate heuristics for MIDS in cubic and at most cubic graphs, based on greedy and local search techniques.

Then, we consider graphs of bounded degree B and B-regular graphs, for B ≥ 4. In particular, the greedy phase proposed for at most cubic graphs is extended to any B and iteratively repeated until the degree of the remaining graph is greater than 3. Finally, the algorithm for at most cubic graphs is executed.

Our algorithms achieve approximation ratios:

• 1.923 for cubic graphs;

• 2 for at most cubic and 4-regular graphs;

• (B ²−2B+2)(B+1)/B ²+1 for B-regular graphs, B≥5;

• (B ²−B+1)(B+1)/B ²+1 for graphs of bounded degree B≥4.

Work supported by: the CEE project ALCOM-IT ESPRIT LTR, project no. 20244, “Algorithms and Complexity in Information Technology”; the Italian Project “Algoritmi, Modelli di Calcolo e Strutture Informative”, Ministero dell'Università e della Ricerca Scientifica e Tecnologica.