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The Computer Journal Advance Access originally published online on September 6, 2007
The Computer Journal 2008 51(3):326-362; doi:10.1093/comjnl/bxm052
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© The Author 2007. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Width Parameters Beyond Tree-width and their Applications

Petr Hlineny1,2,*, Sang-il Oum3 7, Detlef Seese4 and Georg Gottlob5,6

1 Faculty of Informatics, Masaryk University, Botanická 68a, 602 00 Brno, Czech Republic
2 VSB, Technical University of Ostrava, Ostrava, Czech Republic
3 School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA
4 Institute AIFB, University Karlsruhe (TH), D-76128 Karlsruhe, Germany
5 Oxford University Computing Laboratory, Parks Road, Oxford OX1 3QD, UK
6 Vienna University of Technology, Vienna, Austria

* Corresponding author: hlineny{at}fi.muni.cz

Received 30 July 2006; revised 20 December 2006

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.

Key Words: graph • complexity • tree-width • branch-width • clique-width • rank-width • hypertree-width • MSO logic

7 Present address: Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada


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