More efficient two-mode stochastic local search for random 3-satisfiability

HSMVS: heuristic search for minimum vertex separator on massive graphs

In graph theory, the problem of finding minimum vertex separator (MVS) is a classic NP-hard problem, and it plays a key role in a number of important applications in practice. The real-world massive graphs are of very large size, which calls for effective approximate methods, especially heuristic search algorithms. In this article, we present a simple yet effective heuristic search algorithm dubbed HSMVS for solving MVS on real-world massive graphs. Our HSMVS algorithm is developed on the basis of an efficient construction procedure and a simple yet effective vertex-selection heuristic. Experimental results on a large number of real-world massive graphs present that HSMVS is able to find much smaller vertex separators than three effective heuristic search algorithms, indicating the effectiveness of HSMVS. Further empirical analyses confirm the effectiveness of the underlying components in our proposed algorithm.

Clause states based configuration checking in local search for satisfiability

Two-mode stochastic local search (SLS) and focused random walk (FRW) are the two most influential paradigms of SLS algorithms for the propositional satisfiability (SAT) problem. Recently, an interesting idea called configuration checking (CC) was proposed to handle the cycling problem in SLS. The CC idea has been successfully used to improve SLS algorithms for SAT, resulting in state-of-the-art solvers. Previous CC strategies for SAT are based on neighboring variables, and prove successful in two-mode SLS algorithms. However, this kind of neighboring variables based CC strategy is not suitable for improving FRW algorithms. In this paper, we propose a new CC strategy which is based on clause states. We apply this clause states based CC (CSCC) strategy to both two-mode SLS and FRW paradigms. Our experiments show that the CSCC strategy is effective on both paradigms. Furthermore, our developed FRW algorithms based on CSCC achieve state-of-the-art performance on a broad range of random SAT benchmarks.