An improved approximation algorithm for capacitated multicast routings in networks

Authors:
Ehab Morsy;Hiroshi Nagamochi
Affiliations:
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo, Kyoto 606-8501, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo, Kyoto 606-8501, Japan
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

Let G=(V,E) be a connected graph such that each edge e@?E is weighted by nonnegative real w(e). Let s be a vertex designated as a source, k be a positive integer, and S@?V be a set of terminals. The capacitated multicast tree routing problem (CMTR) asks to find a partition {Z"1,Z"2,...,Z"@?} of S and a set {T"1,T"2,...,T"@?} of trees of G such that Z"i consists of at most k terminals and each T"i spans Z"i@?{s}. The objective is to minimize @?"i"="1^@?w(T"i), where w(T"i) denotes the sum of weights of all edges in T"i. In this paper, we propose a (3/2+(4/3)@r)-approximation algorithm to the CMTR, where @r is the best achievable approximation ratio for the Steiner tree problem.