Intuitive algorithms and t-vertex cover

Abstract

Many interesting results that improve on the exponential running times of exact algorithms for NP-hard problems have been obtained in recent years. One example that has attracted quite some attention of late is t-Vertex Cover, the problem of finding k nodes that cover at least t edges in a graph. Following the first proof of fixed-parameter tractability, several algorithms for this problem have been presented in rapid succession. We improve on the best known runtime bound, designing and analyzing an intuitive randomized algorithm that takes no more than O(2.0911t n4) steps. In fact, we observe and encourage a renewed vigor towards the design of intuitive algorithms within the community. That is, we make a plea to prefer simple, comprehendable, easy-to-implement and easy-to-verify algorithms at the expense of a more involved analysis over more complicated algorithms that are specifically tailored to ease the analysis. © 2006 Springer-Verlag Berlin/Heidelberg.