Composing fifth species counterpoint music with a variable neighborhood search algorithm

In this paper, a variable neighborhood search (VNS) algorithm is developed and analyzed that can generate fifth species counterpoint fragments. The existing species counterpoint rules are quantified and form the basis of the objective function used by the algorithm. The VNS developed in this research is a local search metaheuristic that starts from a randomly generated fragment and gradually improves this solution by changing one or two notes at a time. An in-depth statistical analysis reveals the significance as well as the optimal settings of the parameters of the VNS. The algorithm has been implemented in a user-friendly software environment called Optimuse. Optimuse allows a user to input basic characteristics such as length, key and mode. Based on this input, a fifth species counterpoint fragment is generated by the system that can be edited and played back immediately.     

Parameterized Two-Player Nash Equilibrium

We study the problem of computing Nash equilibria in a two-player normal form (bimatrix) game from the perspective of parameterized complexity. Recent results proved hardness for a number of variants, when parameterized by the support size. We complement those results, by identifying three cases in which the problem becomes fixed-parameter tractable. Our results are based on a graph-theoretic representation of a bimatrix game, and on applying graph-theoretic tools on this representation.