Computing a Near-Maximum Independent Set in Dynamic Graphs

Abstract

As a fundamental NP-hard problem in graph theory, the maximum independent set (MIS) has attracted a lot of efforts to improve the time efficiency. However, most graphs in real scenarios are usually changing over time. But the previous studies take the stationary graphs as input, the computation of MIS in dynamic graphs receives little attention. Since computing the exact MIS is intractable, we compute the high-quality (large-size) independent set for dynamic graphs in this paper, where 4 graph updating operations are allowed: adding or deleting a vertex or an edge. Based on two state-of-the-art reduction rules that are designed for static graphs, we propose a novel scheme, i.e., dependency graph based independent set computation, which can support computing the high-quality independent set on the basis of the previous result rather than calculating from scratch. Moreover, a dynamic searching strategy is devised to improve time efficiency. In order to make it more useful in practical applications, we devise an effective yet efficient method to deal with the batch update. To confirm the effectiveness and efficiency of the proposed methods, we conduct extensive experiments over both real and synthetic datasets.