Efficient Algorithm for the Paired-Domination Problem in Convex Bipartite Graphs

Let G = (V, E) be a graph without isolated vertices. A matching in G is a set of independent edges in G. A perfect matching M in G is a matching such that every vertex of G is incident to an edge of M . A set S ⊆ V is a paired-dominating set of G if every vertex not in S is adjacent to a vertex in S, and if the subgraph induced by S contains a perfect matching. The paired-domination problem is to find a paired-dominating set of G with minimum cardinality. The paired-domination problem on bipartite graphs has been shown to be NP-complete. A bipartite graph G = (U, W, E) is convex if there exists an ordering of the vertices of W such that, for each u ∈ U , the neighbors of u are consecutive in W . In this paper, we present an O(|U | log |U |)-time algorithm to solve the paired-domination problem in convex bi-