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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Bibliographic Details
Published in:Information processing letters Vol. 140; pp. 8 - 12
Main Authors: Fomin, Fedor V., Lokshtanov, Daniel, Panolan, Fahad, Saurabh, Saket, Zehavi, Meirav
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2018
Subjects:
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
Online Access:Get full text
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Summary: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