Planar k-path in subexponential time and polynomial space

Authors:
Daniel Lokshtanov;Matthias Mnich;Saket Saurabh
Affiliations:
University of California, San Diego;International Computer Science Institute, Berkeley;The Institute of Mathematical Sciences, Chennai, India
Venue:
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2011

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Abstract

In the k-Path problem we are given an n-vertex graph G together with an integer k and asked whether G contains a path of length k as a subgraph. We give the first subexponential time, polynomial space parameterized algorithm for k-Path on planar graphs, and more generally, on H-minor-free graphs. The running time of our algorithm is $O(2^{O(\sqrt{k}\log^2 k)}n^{O(1)})$ .