Dekel Tsur

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 O^⁎(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.