Faster deterministic parameterized algorithm for k-PATH

In the k-PATH problem, the input is a directed graph G and an integer k >= 1, and the goal is to decide whether there is a simple directed path in G with exactly k vertices. We give a deterministic algorithm for k-PATH with time complexity 0*(2.554(k)). This improves the previously best deterministic algorithm for this problem of Zehavi [ESA 2015] whose time complexity is O*(2.597(k)). The technique used by our algorithm can also be used to obtain faster deterministic algorithms for k-TREE, r-DIMENSIONAL k-MATCHING, GRAPH MOTIF, and PARTIAL COVER. (C) 2019 Elsevier B.V. All rights reserved.