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Improved Approximation Algorithms for the Quality of Service Multicast Tree Problem

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Abstract

The Quality of Service Multicast Tree Problem is a generalization of the Steiner tree problem which appears in the context of multimedia multicast and network design. In this generalization, each node possesses a rate and the cost of an edge with length l in a Steiner tree T connecting the source to non-zero rate nodes is l · re, where re is the maximum node rate in the component of T-{e} that does not contain the source. The best previously known approximation ratios for this problem (based on the best known approximation factor of 1.549 for the Steiner tree problem in networks) are 2.066 for the case of two non-zero rates and 4.212 for the case of an unbounded number of rates. In this paper we give improved approximation algorithms with ratios of 1.960 and 3.802, respectively. When the minimum spanning tree heuristic is used for finding approximate Steiner trees, then the previously best known approximation ratios of 2.667 for two non-zero rates and 5.542 for an unbounded number of rates are reduced to 2.414 and 4.311, respectively.

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Authors and Affiliations

  1. Department of Computer Science, University of Bonn, Bonn 53117, Germany

    Marek Karpinski

  2. Department of Computer Science and Engineering, University of Connecticut, 371 Fairfield Rd., Unit 2155, Storrs, CT 06269-2155, USA

    Ion I. Mandoiu

  3. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Boston, MA 02139-4307, USA

    Alexander Olshevsky

  4. Computer Science Department, Georgia State University, Atlanta, GA 30303,, USA

    Alexander Zelikovsky

Authors
  1. Marek Karpinski
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  2. Ion I. Mandoiu
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  3. Alexander Olshevsky
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  4. Alexander Zelikovsky
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Corresponding authors

Correspondence to Marek Karpinski, Ion I. Mandoiu, Alexander Olshevsky or Alexander Zelikovsky.

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Karpinski, M., Mandoiu, I., Olshevsky, A. et al. Improved Approximation Algorithms for the Quality of Service Multicast Tree Problem. Algorithmica 42, 109–120 (2005). https://doi.org/10.1007/s00453-004-1133-y

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  • DOI: https://doi.org/10.1007/s00453-004-1133-y

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