This paper presents the application of metaheuristic methods to the minimum crossing number problem for the first time. These algorithms including particle swarm optimization, improved ray optimization, colliding bodies optimization and enhanced colliding bodies optimization. For each method, a pseudo code is provided. The crossing number problem is NP-hard and has important applications in eng...

Boolean games are a compact and expressive class of games, based on propositional logic. However, Boolean games are computationally complex: checking for the existence of pure Nash equilibria in Boolean games is Σp2-complete, and it is co-NP-complete to check whether a given outcome for a Boolean game is a pure Nash equilibrium. In this paper, we consider two possible avenues to tractability in...

We present some complexity results on checking necessary efficiency in interval multiobjective linear programming. Supposing that objective function coefficients perturb within prescribed intervals, a feasible point x is called necessarily efficient if it is efficient for all instances of interval data. We show that the problem of checking necessary efficiency is co-NP-complete even for the cas...

The classes of P-, P 0-, R 0-, semimonotone, strictly semimonotone, column suucient, and nondegenerate matrices play important roles in studying solution properties of equations and complementarity problems and conver-gence/complexity analysis of methods for solving these problems. It is known that the problem of deciding whether a square matrix with integer/rational entries is a P-(or nondegen...

The problem of determining whether two given finite graphs are isomorphic is easily seen to belong to the class NP. But up to now, no polynomial time algorithm is known. On the other hand, no NP-completeness proof is known either. That is, GRAPH ISOMORPHISM is one of the few “open problems” in NP according to Garey and Johnson’s terminology [9]. Note that GRAPH ISOMORPHISM is already mentioned ...

Given an H-polytope P and a V-polytope Q, the decision problem whether P is contained in Q is co-NP-complete. This hardness remains if P is restricted to be a standard cube and Q is restricted to be the affine image of a cross polytope. While this hardness classification by Freund and Orlin dates back to 1985, there seems to be only limited progress on that problem so far. Based on a formulatio...