Approximate Min-Max Theorems of Steiner Rooted-Orientations of Hypergraphs
Tamas Kiraly
Lap Chi Lau
MTA-ELTE Egervary Res. Group, Eotvos Lorand Univ., Budapest;
This paper appears in: Foundations of Computer Science, 2006. FOCS '06. 47th Annual IEEE Symposium on
Publication Date: Oct. 2006
On page(s): 283-292
Location: Berkeley, CA,
ISSN: 0272-5428
ISBN: 0-7695-2720-5
INSPEC Accession Number: 9297298
Digital Object Identifier: 10.1109/FOCS.2006.12
Current Version Published: 2006-12-19
Abstract
Given an undirected hypergraph and a subset of vertices S sube V with a specified root vertex r isin S, the Steiner rooted-orientation problem is to find an orientation of all the hyperedges so that in the resulting directed hypergraph the "connectivity" from the root r to the vertices in S is maximized. This is motivated by a multicasting problem in undirected networks as well as a generalization of some classical problems in graph theory. The main results of this paper are the following approximate min-max relations: middot Given an undirected hypergraph H, if S is 2k-hyperedge-connected in H, then H has a Steiner rooted k-hyperarc-connected orientation. middot Given an undirected graph G, if S is 2k-element-connected in G, then G has a Steiner rooted k-element-connected orientation. Both results are tight in terms of the connectivity bounds. These also give polynomial time constant factor approximation algorithms for both problems. The proofs are based on submodular techniques, and a graph decomposition technique used in the Steiner tree packing problem. Some complementary hardness results are presented at the end
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