Paper Info
Title
Exact Algorithms for Minimum Weighted Dominating Induced Matching
Abstract
Say that an edge of a graph G dominates itself and every other edge sharing a vertex of it. An edge dominating set of a graph $$G=(V,E)$$G=(V,E) is a subset of edges $$E' \\subseteq E$$Eź⊆E which dominates all edges of G. In particular, if every edge of G is dominated by exactly one edge of $$E'$$Eź then $$E'$$Eź is a dominating induced matching. It is known that not every graph admits a dominating induced matching, while the problem to decide if it does admit it is NP-complete. In this paper we consider the problems of counting the number of dominating induced matchings and finding a minimum weighted dominating induced matching, if any, of a graph with weighted edges. We describe three exact algorithms for general graphs. The first runs in linear time for a given vertex dominating set of fixed size of the graph. The second runs in polynomial time if the graph admits a polynomial number of maximal independent sets. The third one is an $$O^*(1.1939^n)$$Oź(1.1939n) time and polynomial (linear) space, which improves over the existing algorithms for exactly solving this problem in general graphs.
Year
DOI
Venue
2017
10.1007/s00453-015-0095-6
Algorithmica
Keywords
DocType
Volume
Exact algorithms,Graph theory,Dominating induced matchings
Journal
77
Issue
ISSN
Citations 
3
0178-4617
3
PageRank 
References 
Authors
0.39
22
3
Name
Order
Citations
PageRank
Min Chih Lin125921.22
Michel J. Mizrahi2222.98
Jayme L. Szwarcfiter354645.97