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Elsevier, Journal of Algorithms in Cognition, Informatics and Logic, 2(18), p. 238-255

DOI: 10.1006/jagm.1995.1009

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Approximating Treewidth, Pathwidth, Frontsize, and Shortest Elimination Tree

Journal article published in 1995 by Hans L. Bodlaender ORCID, John R. Gilbert, Hjálmtyr Hafsteinsson, Ton Kloks
This paper is available in a repository.
This paper is available in a repository.

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Abstract

Various parameters of graphs connected to sparse matrix factorization and other applications can be approximated using an algorithm of Leighton et al. that finds vertex separators of graphs. The approximate values of the parameters, which include minimum front size, treewidth, pathwidth, and minimum elimination tree height, are no more than O(logn) (minimum front size and treewidth) and O(log^2 n) (pathwidth and minimum elimination tree height) times the optimal values. In addition, we show that unless P = NP there are no absolute approximation algorithms for any of the parameters.