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Fast approximation of minimum multicast congestion – Implementation VERSUS Theory

Published online by Cambridge University Press:  15 December 2004

Andreas Baltz  and
Anand Srivastav
Andreas Baltz
Affiliation:
Mathematisches Seminar, Bereich II, Christian-Albrechts-Universität zu Kiel, Christian-Albrechts-Platz 4, D-24118 Kiel, Germany; aba@numerik.uni-kiel.de.
Anand Srivastav
Affiliation:
Mathematisches Seminar, Bereich II, Christian-Albrechts-Universität zu Kiel, Christian-Albrechts-Platz 4, D-24118 Kiel, Germany; asr@numerik.uni-kiel.de.
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Abstract

The problem of minimizing the maximum edge congestion in a multicast communication network generalizes the well-known NP-hard multicommodity flow problem. We give the presently best theoretical approximation results as well as efficient implementations. In particular we show that for a network with m edges and k multicast requests, an r(1 + ε)(rOPT + exp(1)lnm)-approximation can be computed in O(kmε-2lnklnm) time, where β bounds the time for computing an r-approximate minimum Steiner tree. Moreover, we present a new fast heuristic that outperforms the primal-dual approaches with respect to both running time and objective value.

Keywords

Combinatorial optimizationapproximation algorithms.
Type
Research Article
Information
RAIRO - Operations Research , Volume 38 , Issue 4 , October 2004 , pp. 319 - 344
Copyright
© EDP Sciences, 2004

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