Asymptotically Faster Algorithms for Parameterized FACE COVER.
Faisal N. Abu-Khzam, Henning Fernau, Michael Allen Langston · 2005
Abstract. The parameterized complexity of the face cover problem is considered. The input to this problem is a plane graph, G, ofordern. The question asked is whether, for any fixed k, there exists a set of k or fewer vertices whose boundaries collectively cover (contain) every vertex in G. The fastest previously-published face cover algorithm is achieved with the bounded search tree technique, in which branching requires O(5 k + n 2) time. In this paper, a structure theorem of Aksionov et al. is combined with a detailed case analysis to produce a face cover algorithm that runs in O(4.5414 k +n 2) time. 1