Approximation algorithms for general packing problems and their application to the multicast congestion problem |
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Authors: | Klaus Jansen Hu Zhang |
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Institution: | 1. Institut für Informatik, Universit?t Kiel, Olshausenstra?e 40, 24098, Kiel, Germany 2. Department of Computing and Software, McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4K1, Canada
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Abstract: | In this paper we present approximation algorithms based on a Lagrangian decomposition via a logarithmic potential reduction
to solve a general packing or min–max resource sharing problem with M non-negative convex constraints on a convex set B. We generalize a method by Grigoriadis et al. to the case with weak approximate block solvers (i.e., with only constant,
logarithmic or even worse approximation ratios). Given an accuracy , we show that our algorithm needs calls to the block solver, a bound independent of the data and the approximation ratio of the block solver. For small approximation
ratios the algorithm needs calls to the block solver. As an application we study the problem of minimizing the maximum edge congestion in a multicast
communication network. Interestingly the block problem here is the classical Steiner tree problem that can be solved only
approximately. We show how to use approximation algorithms for the Steiner tree problem to solve the multicast congestion
problem approximately.
This work was done in part when the second author was studying at the University of Kiel.
This paper combines our extended abstracts of the 2nd IFIP International Conference on Theoretical Computer Science, TCS 2002, Montréal, Canada and the 3rd Workshop on Approximation and Randomization Algorithms in Communication Networks, ARACNE 2002, Roma, Italy. This research was supported in part by the DFG - Graduiertenkolleg, Effiziente Algorithmen und
Mehrskalenmethoden; by the EU Thematic Network APPOL I + II, Approximation and Online Algorithms, IST-1999-14084 and IST-2001-32007;
by the EU Research Training Network ARACNE, Approximation and Randomized Algorithms in Communication Networks, HPRN-CT-1999-00112;
by the EU Project CRESCCO, Critical Resource Sharing for Cooperation in Complex Systems, IST-2001-33135. The second author
was also supported by an MITACS grant of Canada; and by the NSERC Discovery Grant DG 5-48923. |
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Keywords: | 68W25 68W40 90C05 90C25 68M10 |
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