Parametric duality and kernelization: Lower bounds and upper bounds on kernel size

DSpace/Manakin Repository

LDR Home . . . Xia, Ge Publications of Ge Xia View Item

Parametric duality and kernelization: Lower bounds and upper bounds on kernel size

Show simple item record


dc.contributor.author Kanj, I. A.
dc.contributor.author Fernau, H.
dc.contributor.author Chen, J.
dc.contributor.author Xia, Ge
dc.date.accessioned 2010-02-26T15:25:46Z
dc.date.available 2010-02-26T15:25:46Z
dc.date.issued 2007
dc.identifier.citation Chen, J., et al. (2007.) "Parametric duality and kernelization: Lower bounds and upper bounds on kernel size." SIAM Journal on Computing 37 (4): 1077-1106. en_US
dc.identifier.uri http://hdl.handle.net/10385/623
dc.description.abstract Determining whether a parameterized problem is kernelizable and has a small kernel size has recently become one of the most interesting topics of research in the area of parameterized complexity and algorithms. Theoretically, it has been proved that a parameterized problem is kernelizable if and only if it is fixed-parameter tractable. Practically, applying a data reduction algorithm to reduce an instance of a parameterized problem to an equivalent smaller instance (i.e., a kernel) has led to very efficient algorithms and now goes hand-in-hand with the design of practical algorithms for solving NP-hard problems. Well-known examples of such parameterized problems include the vertex cover problem, which is kernelizable to a kernel of size bounded by 2k, and the planar dominating set problem, which is kernelizable to a kernel of size bounded by 335k. In this paper we develop new techniques to derive upper and lower bounds on the kernel size for certain parameterized problems. In terms of our lower bound results, we show, for example, that unless P = NP, planar vertex cover does not have a problem kernel of size smaller than 4k/3, and planar independent set and planar dominating set do not have kernels of size smaller than 2k. In terms of our upper bound results, we further reduce the upper bound on the kernel size for the planar dominating set problem to 67k, improving significantly the 335k previous upper bound given by Alber, et al. This latter result is obtained by introducing a new set of reduction and coloring rules, which allows the derivation of nice combinatorial properties in the kernelized graph leading to a tighter bound on the size of the kernel. The paper also shows how this improved upper bound yields a simple and competitive algorithm for the planar dominating set problem. en_US
dc.description.uri 10.1137/050646354
dc.publisher SIAM Journal on Computing en_US
dc.subject kernel en_US
dc.subject dominating set en_US
dc.subject planar graph en_US
dc.subject independent set en_US
dc.subject vertex cover en_US
dc.subject parameterized algorithm en_US
dc.title Parametric duality and kernelization: Lower bounds and upper bounds on kernel size en_US
dc.type Article en_US

Files in this item

Files Size Format View
Xia-SIAMJournalonComputing-2007-vol37-no4.pdf 345.1Kb PDF View/Open

This item appears in the following Collection(s)

Show simple item record

Search LDR


Advanced Search

Browse

My Account