Towards Computing a Near-Maximum Weighted Independent Set on Massive Graphs

The vertices in many graphs are weighted unequally in real scenarios, but the previous studies on the maximum independent set (MIS) ignore the weights of vertices. Therefore, the weight of an MIS may not necessarily be the largest. In this paper, we study the problem of maximum weighted independent set (MWIS) that is defined as the set of independent vertices with the largest weight. Since it is intractable to deliver the exact solution for large graphs, we design a reducing and tie-breaking framework to compute a near-maximum weighted independent set. The reduction rules are critical to reduce the search space for both exact and greedy algorithms as they determine the vertices that are definitely (or not) in the MWIS while preserving the correctness of solutions. We devise a set of novel reductions including low-degree reductions and high-degree reductions for general weighted graphs. Extensive experimental studies over real graphs confirm that our proposed method outperforms the state-of-the-arts significantly in terms of both effectiveness and efficiency.