A linear time algorithm for computing a minimum paired-dominating set of a convex bipartite graph

A set DD of vertices of a graph G=(V,E)G=(V,E) is a dominating set   of GG if every vertex in V∖DV∖D has at least one neighbor in DD. A dominating set DD of GG is a paired-dominating set   of GG if the induced subgraph, G[D]G[D], has a perfect matching. The paired-domination problem   is for a given graph GG and a positive integer kk to answer if GG has a paired-dominating set of size at most kk. The paired-domination problem is known to be NP-complete even for bipartite graphs. In this paper, we propose a linear time algorithm to compute a minimum paired-dominating set of a convex bipartite graph.