Kernelization as Heuristic Structure for the Vertex Cover Problem

Abstract

For solving combinatorial optimisation problems, exact methods accurately exploit the structure of the problem but are tractable only up to a certain size; approximation or heuristic methods are tractable for very large problems but may possibly be led into a bad solution. A question that arises is, From where can we obtain knowledge of the problem structure via exact methods that can be exploited on large-scale problems by heuristic methods? We present a framework that allows the exploitation of existing techniques and resources to integrate such structural knowledge into the Ant Colony System metaheuristic, where the structure is determined through the notion of kernelization from the field of parameterized complexity. We give experimental results using vertex cover as the problem instance, and show that knowledge of this type of structure improves performance beyond previously defined ACS algorithms.