On Approximating Minimum Vertex Cover for Graphs with Perfect Matching

It has been a challenging open problem whether there is a polynomial time approximation algorithm for the Vertex Cover problem whose approximation ratio is bounded by a constant less than 2. In this paper, we study the Vertex Cover problem on graphs with perfect matching (shortly, VC-PM). We show that if the VC-PM problem has a polynomial time approximation algorithm with approximation ratio bounded by a constant less than 2, then so does the Vertex Cover problem on general graphs. Approximation algorithms for VC-PM are developed, which induce improvements over previously known algorithms on sparse graphs.

• Type: Conference
• Year: 2000
• Where: ISAAC
• Authors: Jianer Chen, Iyad A. Kanj
• Keywords: Algorithms, ISAAC 2000, Polynomial Time Approximation, Time Approximation Algorithm, Vertex Cover Problem