NDLI: A Generalization of AT-Free Graphs and a Generic Algorithm for Solving Triangulation Problems

Content Provider	Springer Nature Link
Copyright Year	2001
Abstract	A subset A of the vertices of a graph G is an asteroidal set if for each vertex a ∈ A a connected component of G-N[a] exists containing A\backslash{a} . An asteroidal set of cardinality three is called asteriodal triple and graphs without an asteriodal triple are called AT-free . The maximum cardinality of an asteroidal set of G , denoted by \an(G) , is said to be the asteriodal number of G . We present a scheme for designing algorithms for triangulation problems on graphs. As a consequence, we obtain algorithms to compute graph parameters such as treewidth, minimum fill-in and vertex ranking number. The running time of these algorithms is a polynomial (of degree asteriodal number plus a small constant) in the number of vertices and the number of minimal separators of the input graph.
Starting Page	594
Ending Page	610
Page Count	17
File Format	PDF
ISSN	01784617
Journal	Algorithmica
Volume Number	32
Issue Number	4
e-ISSN	14320541
Language	English
Publisher	Springer-Verlag
Publisher Date	2002-06-10
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Algorithm Analysis and Problem Complexity Theory of Computation Mathematics of Computing Algorithms Computer Systems Organization and Communication Networks Data Structures, Cryptology and Information Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Science Applications

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A Generalization of AT-Free Graphs and a Generic Algorithm for Solving Triangulation Problems