Kernel bounds for path and cycle problems

Connectivity problems like k-Path and k-Disjoint Paths relate to many important milestones in parameterized complexity, namely the Graph Minors Project, color coding, and the recent development of techniques for obtaining kernelization lower bounds. This work explores the existence of polynomial ker...

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Bibliographic Details
Published inTheoretical computer science Vol. 511; pp. 117 - 136
Main Authors Bodlaender, Hans L., Jansen, Bart M.P., Kratsch, Stefan
Format Journal Article
LanguageEnglish
Published Elsevier B.V 04.11.2013
Subjects
Graphs
Kernelization
Parameterized complexity
Path and cycle problems
Upper and lower bounds
Graphs
Path and cycle problems
Parameterized complexity
Upper and lower bounds
Kernelization
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ISSN0304-3975
1879-2294
DOI10.1016/j.tcs.2012.09.006

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Summary:Connectivity problems like k-Path and k-Disjoint Paths relate to many important milestones in parameterized complexity, namely the Graph Minors Project, color coding, and the recent development of techniques for obtaining kernelization lower bounds. This work explores the existence of polynomial kernels for various path and cycle problems, by considering nonstandard parameterizations. We show polynomial kernels when the parameters are a given vertex cover, a modulator to a cluster graph, or a (promised) max leaf number. We obtain lower bounds via cross-composition, e.g., for Hamiltonian Cycle and related problems when parameterized by a modulator to an outerplanar graph.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2012.09.006