Long directed (s,t)-path: FPT algorithm

Given a digraph G, two vertices s,t∈V(G) and a non-negative integer k, the Long Directed(s,t)-Path problem asks whether G has a path of length at least k from s to t. We present a simple algorithm that solves Long Directed(s,t)-Path in time O⋆(4.884k). This results also in an improvement upon the pr...

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Vydané v:	Information processing letters Ročník 140; s. 8 - 12
Hlavní autori:	Fomin, Fedor V., Lokshtanov, Daniel, Panolan, Fahad, Saurabh, Saket, Zehavi, Meirav
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 01.12.2018
Predmet:	Long directed ([formula omitted])-path Long directed cycle Parameterized algorithm Long directed (s,t)-path Parameterized algorithm Long directed cycle
ISSN:	0020-0190, 1872-6119
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Popis
Shrnutí:	Given a digraph G, two vertices s,t∈V(G) and a non-negative integer k, the Long Directed(s,t)-Path problem asks whether G has a path of length at least k from s to t. We present a simple algorithm that solves Long Directed(s,t)-Path in time O⋆(4.884k). This results also in an improvement upon the previous fastest algorithm for Long Directed Cycle. •Single-exponential time parameterized algorithm for long directed (s, t)-path.•The algorithm is simple and intuitive.•Consequently, we also obtain an improvement for long directed cycle.
ISSN:	0020-0190 1872-6119
DOI:	10.1016/j.ipl.2018.04.018