Volume 38, Number 4, October-December 2004
|Page(s)||319 - 344|
|Published online||15 December 2004|
Fast approximation of minimum multicast congestion – Implementation VERSUS Theory
Mathematisches Seminar, Bereich II,
Christian-Albrechts-Universität zu Kiel,
Christian-Albrechts-Platz 4, D-24118 Kiel, Germany; email@example.com.
2 Mathematisches Seminar, Bereich II, Christian-Albrechts-Universität zu Kiel, Christian-Albrechts-Platz 4, D-24118 Kiel, Germany; firstname.lastname@example.org.
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.
Mathematics Subject Classification: 68W25 / 90C27
Key words: Combinatorial optimization / approximation algorithms.
© EDP Sciences, 2004
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