Abstract: We consider the problem of computing a large stable matching in a bipartite graph G = (A U B, E) where each vertex ranks its neighbors in an order of preference, perhaps involving ties.The goal is to compute a large stable matching. It is known that computing a maximum size stable matching is APX-hard. We present an improved approximation algorithm for the case when ties are present only in the preference lists of vertices in B. This case is also APX-hard and the current best approximation ratio known here is 25/17, we show a simple linear time algorithm that achieves an approximation ratio of 22/15.
