Querying Maximum Quasi-independent Set by Pay-and-Recycle

In the paper, we study the problem of computing a maximum quasi-independent set that admits $k$ conflict edges at most but contains the set of query vertices $S$. It generalizes the task of finding a maximum independent set (shorted as MIS) for a given graph. Due to the intractable hardness of computing an exact solution, delivering a high-quality approximate solution within a time budget can be accepted. The existing algorithms for the maximum quasi-independent set are organized in two phases, namely near-MIS initialization and edge expansion (i.e., deleting edges). As both of the two phases adopt greedy strategies, error propagation degrades the quality of delivered answer sets. In contrast, we develop a novel pay-and-recycle approach interleaving the above two phases. Instead of making greedy peelings when no reduction rules can be applied, we delete an edge (i.e., edge expansion) to create opportunities for applying reduction rules. To enhance the performance, the wasted edges are detected and recycled for further expansion. Moreover, we propose an effective method to guide edge expansion based on offline samples. Extensive empirical studies show that our proposed method outperforms the state-of-the-art algorithm in finding larger quasi-independent sets.