Embeddings of k-Connected Graphs of Pathwidth k
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BibTeX
@MISC{Gupta_embeddingsof,
author = {Arvind Gupta and Naomi Nishimura and Andrzej Proskurowski and Prabhakar Ragde and Prabhakar},
title = {Embeddings of k-Connected Graphs of Pathwidth k},
year = {}
}
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Abstract
. We present O(n 3 ) embedding algorithms (generalizing subgraph isomorphism) for classes of graphs of bounded pathwidth, where n is the number of vertices in the graph. These include the rst polynomialtime algorithm for minor containment and the rst O(n c ) algorithm (c a constant independent of k) for topological embedding of graphs from subclasses of partial k-trees. Of independent interest are structural properties of k-connected graphs of bounded pathwidth on which our algorithms are based. We also describe special cases which reduce to various generalizations of string matching, permitting more ecient solutions. 1 Introduction Many fundamental problems in a diverse set of research areas can be characterized as graph embedding problems, where data is represented as graphs and patterns can be detected by nding smaller graphs in larger ones. Classic patternmatching problems make use of the subgraph isomorphism problem, namely, the problem of determining whether ther...
