Approximation Algorithm Based on Chain Implication for Constrained Minimum Vertex Covers in Bipartite Graphs

Abstract

The constrained minimum vertex cover problem on bipartite graphs (the Min-CVCB problem) is an important NP-complete problem. This paper presents a polynomial time approximation algorithm for the problem based on the technique of chain implication. For any given constant ɛ > 0, if an instance of the Min-CVCB problem has a minimum vertex cover of size (k u , k l ), our algorithm constructs a vertex cover of size (k * u , k * l ), satisfying max {k * u /k u , k * l /k l } ≤ 1 + ɛ.