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Approximation Algorithms for Multicast Routings in a Network with Multi-Sources Ehab MOSRY Hiroshi NAGAMOCHI Publication IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Vol.E90-A No.5 pp.900-906 Publication Date: 2007/05/01 Online ISSN: 1745-1337 DOI: 10.1093/ietfec/e90-a.5.900 Print ISSN: 0916-8508 Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications) Category: Keyword: approximation algorithm, facility location problem, graph algorithm, multicast routing problem, network optimization, tree cover, Full Text: PDF(195.1KB)>>
Summary: We consider the capacitated multi-source multicast tree routing problem (CMMTR) in an undirected graph G=(V,E) with a vertex set V, an edge set E and an edge weight w(e) ≥ 0, e ∈ E. We are given a source set S ⊆ V with a weight g(e) ≥ 0, e ∈ S, a terminal set M ⊆ V-S with a demand function q : M → R+, and a real number κ > 0, where g(s) means the cost for opening a vertex s ∈ S as a source in a multicast tree. Then the CMMTR asks to find a subset S′⊆ S, a partition {Z1,Z2,...,Zl} of M, and a set of subtrees T1,T2,...,Tl of G such that, for each i, ∑t∈Ziq(t) ≤ κ and Ti spans Zi∪{s} for some s ∈ S′. The objective is to minimize the sum of the opening cost of S′and the constructing cost of {Ti}, i.e., ∑s∈S′g(s)+  w(Ti), where w(Ti) denotes the sum of weights of all edges in Ti. In this paper, we propose a (2ρUFL+ρST)-approximation algorithm to the CMMTR, where ρUFL and ρST are any approximation ratios achievable for the uncapacitated facility location and the Steiner tree problems, respectively. When all terminals have unit demands, we give a ((3/2)ρUFL+(4/3)ρST)-approximation algorithm. | ||||||||||
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