Optimal Hypergraph Tree-Realization

Consider a hyperstar H and a function ω assigning a non-negative weight to every unordered pair of vertices of H and satisfying the following restriction: for any three vertices u,v,x such that u and v belong to the same set of hyperedges, ω ({u,x}) = ω ({v,x}). We provide an efficient method that f...

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Bibliographic Details
Published inGraph-Theoretic Concepts in Computer Science pp. 261 - 270
Main Authors Korach, Ephraim, Razgon, Margarita
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 2005
SeriesLecture Notes in Computer Science
Subjects
Bipartite Match
Current Match
Directed Acyclic Graph
Linear Order
Unordered Pair
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ISBN3540310002
9783540310006
ISSN0302-9743
1611-3349
DOI10.1007/11604686_23

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Summary:Consider a hyperstar H and a function ω assigning a non-negative weight to every unordered pair of vertices of H and satisfying the following restriction: for any three vertices u,v,x such that u and v belong to the same set of hyperedges, ω ({u,x}) = ω ({v,x}). We provide an efficient method that finds a tree-realization T of H which has the maximum weight subject to the minimum number of leaves. We transform the problem to the construction of an optimal degree-constrained spanning arborescence of a non-negatively weighted directed acyclic graph (DAG). The latter problem is a special case of the weighted matroid intersection problem. We propose a faster method based on finding the maximum weighted bipartite matching.
ISBN:3540310002
9783540310006
ISSN:0302-9743
1611-3349
DOI:10.1007/11604686_23