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Algorithms for Vertex Partitioning Problems on Partial k-Trees

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Telle, Jan Arne Proskurowski, Andrzej
Copyright Year	1997
Abstract	In this paper, we consider a large class of vertex partitioning problems and apply to them the theory of algorithm design for problems restricted to partial k-trees. We carefully describe the details of algorithms and analyze their complexity in an attempt to make the algorithms feasible as solutions for practical applications.We give a precise characterization of vertex partitioning problems, which include domination, coloring and packing problems, and their variants. Several new graph parameters are introduced as generalizations of classical parameters. This characterization provides a basis for a taxonomy of a large class of problems, facilitating their common algorithmic treatment and allowing their uniform complexity classification.We present a design methodology of practical solution algorithms for generally $\NP$-hard problems when restricted to partial k-trees (graphs with treewidth bounded by k). This "practicality" accounts for dependency on the parameter k of the computational complexity of the resulting algorithms.By adapting the algorithm design methodology on partial k-trees to vertex partitioning problems, we obtain the first algorithms for these problems with reasonable time complexity as a function of treewidth. As an application of the methodology, we give the first polynomial-time algorithm on partial k-trees for computation of the Grundy number.
Starting Page	529
Ending Page	550
Page Count	22
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480194275825
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	4
Volume Number	10
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-01
Access Restriction	Subscribed
Subject Keyword	algorithms Analysis of algorithms and problem complexity Graph theory graph partitioning treewidth implementations
Content Type	Text
Resource Type	Article
Subject	Mathematics

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