Planar k-Path in Subexponential Time and Polynomial Space

Daniel Lokshtanov, Matthias Mnich, Saket Saurabh

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

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)})o(2^{o(\sqrt{k}\log^2 k)}n^{o(1)}).
Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science
Subtitle of host publication37th International Workshop, WG 2011 Tepla Monastery, Czech Republic, June 2011 Revised Papers
EditorsPetr Kolman, Jan Kratochvil
PublisherSpringer
Pages262-270
ISBN (Electronic)978-3-642-25870-1
ISBN (Print)978-3-642-25869-5
DOIs
Publication statusPublished - 2011
Externally publishedYes

Publication series

SeriesLecture Notes in Computer Science
Volume6986

Cite this

Lokshtanov, D., Mnich, M., & Saurabh, S. (2011). Planar k-Path in Subexponential Time and Polynomial Space. In P. Kolman, & J. Kratochvil (Eds.), Graph-Theoretic Concepts in Computer Science: 37th International Workshop, WG 2011 Tepla Monastery, Czech Republic, June 2011 Revised Papers (pp. 262-270). Springer. Lecture Notes in Computer Science, Vol.. 6986 https://doi.org/10.1007/978-3-642-25870-1_24