Optimal hypergraph tree-realization

Authors:
Ephraim Korach;Margarita Razgon
Affiliations:
Department of Industrial Engineering and Management, Ben-Gurion University of the negev, Beer-Sheva, Israel;Department of Industrial Engineering and Management, Ben-Gurion University of the negev, Beer-Sheva, Israel
Venue:
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Year:
2005

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Abstract

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.