Given a graph G, a non-negative integer k, and a weight function that maps each vertex in G to a positive real number, the Maximum Weighted Budgeted Independent Set (MWBIS) problem is about finding a maximum weighted independent set in G of cardinality at most k. A special case of MWBIS, when the weight assigned to each vertex is equal to its degree in G, is called the Maximum Independent Vertex Coverage (MIVC) problem. In other words, the MIVC problem is about finding an independent set of cardinality at most k with maximum coverage.Since it is a generalization of the well-known Maximum Weighted Independent Set (MWIS) problem, MWBIS too does not have any constant factor polynomial time approximation algorithm assuming P = N P . In this paper, we study MWBIS in the context of bipartite graphs. We show that, unlike MWIS, the MIVC (and thereby the MWBIS) problem in bipartite graphs is NP-hard. Then, we show that the MWBIS problem admits a 1 2 -factor approximation algorithm in the class of bipartite graphs, which matches the integrality gap of a natural LP relaxation.

No abstract