Efficient computation of maximum weighted independent sets on weighted dynamic graph

An independent set is a set of vertices in a graph in which no two vertices are adjacent to each other. The maximum weighted independent set is the independent set with the largest sum of weights in a weighted graph. Considering that existing methods are inefficient when computing the maximum weighted independent set, we propose a combined neighbor reduction rule and a loss value-based greedy strategy to improve the efficiency and increase the weight of the independent set. Additionally, we propose the efficient approximate algorithms for the maximum weighted independent set on dynamic graphs. We decompose the weight change problem into five cases and propose corresponding strategies for each case. Finally, we conduct experiments on 8 real-world datasets to verify the effectiveness and efficiency of the proposed methods.