Efficient Weighted Independent Set Computation over Large Graphs

Abstract

As a well-known optimization problem, the maximum independent set (MIS) has attracted a lot of effort due to its significance in graph theory and wide applications. Nevertheless, the vertices of many graphs are weighted unequally in real scenarios, but the previous studies ignore the intrinsic weights on the graphs. Therefore, the weight of an MIS may not necessary to be the largest. Generalizing the traditional MIS problem, we study the problem of maximum weighted independent set (MWIS) that returns the set of independent vertices with the largest weight in this paper, which is computationally expensive. Following the reduction-and-branching strategy, we propose an exact algorithm to compute the maximum weighted independent set. Since it is intractable to deliver the exact solution for large graphs, we design an efficient greedy algorithm to compute a near-maximum weighted independent set. We devise a set of novel reductions for general weighted graphs. To confirm the effectiveness and efficiency of the proposed methods, we conduct extensive experimental studies over a bunch of real graphs.