NDLI: Approximating Width Parameters of Hypergraphs with Excluded Minors

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Fomin, Fedor V. Golovach, Petr A. Thilikos, Dimitrios M.
Copyright Year	2011
Abstract	The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello in order to extend the concept of hypergraph acyclicity. These notions were further generalized by Grohe and Marx, who introduced the fractional hypertree width of a hypergraph. All these width parameters on hypergraphs are useful for extending the tractability of many problems in database theory and artificial intelligence. In this paper, we study the approximability of (generalized, fractional) hypertree width of sparse hypergraphs where the criterion of sparsity reflects the sparsity of their incidence graphs. Our first step is to prove that the (generalized, fractional) hypertree width of a hypergraph ℋ is constant factor sandwiched by the treewidth of its incidence graph when the incidence graph belongs to some apex-minor-free graph class (the family of apex-minor-free graph classes includes planar graphs and graphs of bounded genus). This determines the combinatorial borderline above in which the notion of (generalized, fractional) hypertree width becomes essentially more general than treewidth, justifying that way its functionality as a hypergraph acyclicity measure. While for more general sparse families of hypergraphs treewidth of incidence graphs and all hypertree width parameters may differ arbitrarily, there are sparse families where a constant factor approximation algorithm is possible. In particular, we give a constant factor approximation polynomial time algorithm for (generalized, fractional) hypertree width on hypergraphs whose incidence graphs belong to some H-minor-free graph class.
Starting Page	1331
Ending Page	1348
Page Count	18
File Format	PDF
ISSN	08954801
DOI	10.1137/080743226
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	3
Volume Number	25
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2011-09-13
Access Restriction	Subscribed
Subject Keyword	approximation minor-free graphs hypergraphs Graph theory Graph algorithms Hypergraphs hypertree width Graph minors
Content Type	Text
Resource Type	Article
Subject	Mathematics

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APPROXIMATING WIDTH PARAMETERS OF HYPERGRAPHS WITH EXCLUDED MINORS (2011)

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