The minimum weighted vertex cover (MWVC) problem is a well known combinatorial optimization problem with important applications. This paper introduces a novel local search algorithm called NuMWVC for MWVC based on three ideas. First, four reduction rules are introduced during the initial construction phase. Second, the configuration checking with aspiration is proposed to reduce cycling problem. Moreover, a self-adaptive vertex removing strategy is proposed to save time.

The Maximum Weight Clique problem (MWCP) is an important generalization of the Maximum Clique problem with wide applications. This paper introduces two heuristics and develops two local search algorithms for MWCP. Firstly, we propose a heuristic called strong configuration checking (SCC), which is a new variant of a recent powerful strategy called configuration checking (CC) for reducing cycling in local search. Based on the SCC strategy, we develop a local search algorithm named LSCC. Moreover, to improve the performance on massive graphs, we apply a low-complexity heuristic called Best from Multiple Selection (BMS) to select the swapping vertex pair quickly and effectively. The BMS heuristic is used to improve LSCC, resulting in the LSCC+BMS algorithm. Experiments show that the proposed algorithms outperform the state-of-the-art local search algorithm MN/TS and its improved version MN/TS+BMS on the standard benchmarks namely DIMACS and BHOSLIB, as well as a wide range of real world massive graphs.

The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of Constraint Satisfaction Problems (#CSP). We consider the random model, i.e. RB model. We prove that phase transition of #CSP does exist as the number of variables approaches infinity and the critical values where phase transitions occur are precisely located. Preliminary experimental results also show that the critical point coincides with the theoretical derivation. Moreover, we propose an approximate algorithm to estimate the expectation value of the solutions number of a given CSP instance of RB model.

We extend the precedence constraints contexts heuristic (hpcc) to a temporal and numeric setting, and propose rules to account precedence constraints among comparison variables and logical variables. Experimental results on benchmark domains show that our extension has the potential to lead to better plan quality than that with the heuristic proposed by Eyerich and others.

In this paper, we investigate the hybrid tractability of binary Quantified Constraint Satisfaction Problems (QCSPs). First, a basic tractable class of binary QCSPs is identified by using the broken-triangle property. In this class, the variable ordering for the broken-triangle property must be same as that in the prefix of the QCSP. Second, we break this restriction to allow that existentially quantified variables can be shifted within or out of their blocks, and thus identify some novel tractable classes by introducing the broken-angle property. Finally, we identify a more generalized tractable class, i.e., the min-of-max extendable class for QCSPs.

The rigorous theoretical analyses of algorithms for #SAT have been proposed in the literature. As we know, previous algorithms for solving #SAT have been analyzed only regarding the number of variables as the parameter. However, the time complexity for solving #SAT instances depends not only on the number of variables, but also on the number of clauses. Therefore, it is significant to exploit the time complexity from the other point of view, i.e. the number of clauses. In this paper, we present algorithms for solving #2-SAT and #3-SAT with rigorous complexity analyses using the number of clauses as the parameter. By analyzing the algorithms, we obtain the new worst-case upper bounds O(1.1892m) for #2-SAT and O(1.4142m) for #3-SAT, where m is the number of clauses.