Width parameters beyond tree-width and their applications

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Besides the very successful concept of tree-width (see [Bodlaender, H. and Koster, A. (2007) Combinatorial optimisation on graphs of bounded treewidth. These are special issues on Parameterized Complexity]), many concepts and parameters measuring the similarity or dissimilarity of structures compared to trees have been born and studied over the past years. These concepts and parameters have proved to be useful tools in many applications, especially in the design of efficient algorithms. Our presented novel look at the contemporary developments of these 'width' parameters in combinatorial structures delivers-besides traditional tree-width and derived dynamic programming schemes-also a number of other useful parameters like branch-width, rank-width (clique-width) or hypertree-width. In this contribution, we demonstrate how 'width' parameters of graphs and generalized structures (such as matroids or hypergraphs), can be used to improve the design of parameterized algorithms and the structural analysis in other applications on an abstract level.
Publisher
OXFORD UNIV PRESS
Issue Date
2008-05
Language
English
Article Type
Review
Keywords

MONADIC 2ND-ORDER LOGIC; BOUNDED CLIQUE-WIDTH; LINEAR-TIME ALGORITHMS; CONSTRAINT-SATISFACTION PROBLEMS; HIERARCHICALLY DEFINED GRAPHS; DISTANCE-HEREDITARY GRAPHS; BRANCH-WIDTH; DECOMPOSABLE GRAPHS; HYPERTREE-WIDTH; RELATIONAL STRUCTURES

Citation

COMPUTER JOURNAL, v.51, no.3, pp.326 - 362

ISSN
0010-4620
DOI
10.1093/comjnl/bxm052
URI
http://hdl.handle.net/10203/90629
Appears in Collection
MA-Journal Papers(저널논문)
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