eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-06-19
13:1
13:13
10.4230/LIPIcs.SEA.2018.13
article
An Efficient Local Search for the Minimum Independent Dominating Set Problem
Haraguchi, Kazuya
1
Otaru University of Commerce, Midori 3-5-21/Otaru, Hokkaido, Japan
In the present paper, we propose an efficient local search for the minimum independent dominating set problem. We consider a local search that uses k-swap as the neighborhood operation. Given a feasible solution S, it is the operation of obtaining another feasible solution by dropping exactly k vertices from S and then by adding any number of vertices to it. We show that, when k=2, (resp., k=3 and a given solution is minimal with respect to 2-swap), we can find an improved solution in the neighborhood or conclude that no such solution exists in O(n Delta) (resp., O(n Delta^3)) time, where n denotes the number of vertices and Delta denotes the maximum degree. We develop a metaheuristic algorithm that repeats the proposed local search and the plateau search iteratively, where the plateau search examines solutions of the same size as the current solution that are obtainable by exchanging a solution vertex and a non-solution vertex. The algorithm is so effective that, among 80 DIMACS graphs, it updates the best-known solution size for five graphs and performs as well as existing methods for the remaining graphs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol103-sea2018/LIPIcs.SEA.2018.13/LIPIcs.SEA.2018.13.pdf
Minimum independent dominating set problem
local search
plateau search
metaheuristics