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European Symposium on Algorithms

ESA 1998: Algorithms — ESA’ 98 pp 429–440Cite as

Nearest Neighbor Load Balancing on Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1461))

Abstract

We design a general mathematical framework to analyze the properties of nearest neighbor balancing algorithms of the diffusion type. Within this framework we develop a new optimal polynomial scheme (OPS) which we show to terminate within a finite number m of steps, where m only depends on the graph and not on the initial load distribution.

We show that all existing diffusion load balancing algorithms, including OPS determine a flow of load on the edges of the graph which is uniquely defined, independent of the method and minimal in the l 2-norm. This result can also be extended to edge weighted graphs.

The l 2-minimality is achieved only if a diffusion algorithm is used as preprocessing and the real movement of load is performed in a second step. Thus, it is advisable to split the balancing process into the two steps of first determining a balancing flow and afterwards moving the load. We introduce the problem of scheduling a flow and present some first results on the approximation quality of local greedy heuristics.

Partly supported by the DFG-Sonderforschungsbereich 376 “Massive Parallelität: Algorithmen, Entwurfsmethoden, Anwendungen” and the EC ESPRIT Long Term Research Project 20244 (ALCOM-IT).

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Paderborn, Fürstenallee 11, D-33102, Paderborn, Germany

    Ralf Diekmann & Burkhard Monien

  2. Department of Mathematics and Institute for Applied Computer Science, University of Wuppertal, D-42097, Wuppertal, Germany

    Andreas Frommer

Authors
  1. Ralf Diekmann
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  2. Andreas Frommer
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  3. Burkhard Monien
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Editor information

Editors and Affiliations

  1. Dipartimento di Elettronica e Informatica, Università di Padova, via Gradenigo 6/A, I-35131, Padova, Italy

    Gianfranco Bilardi  & Geppino Pucci  & 

  2. Department of Electrical Engineering and Computer Science, The University of Illinois at Chicago, 851 South Morgan Street - 1009 SEO, Chicago, IL, 60607-7053, USA

    Gianfranco Bilardi

  3. Dipartimento di Matematica Applicata e Informatica, Università “Cá Foscari” di Venezia, via Torino 155, I-30173, Venezia Mestre, Italy

    Giuseppe F. Italiano

  4. Dipartimento di Matematica Pura e Applicata, Università di Padova, via Belzoni 7, I-35131, Padova, Italy

    Andrea Pietracaprina

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© 1998 Springer-Verlag Berlin Heidelberg

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Diekmann, R., Frommer, A., Monien, B. (1998). Nearest Neighbor Load Balancing on Graphs. In: Bilardi, G., Italiano, G.F., Pietracaprina, A., Pucci, G. (eds) Algorithms — ESA’ 98. ESA 1998. Lecture Notes in Computer Science, vol 1461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68530-8_36

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  • DOI: https://doi.org/10.1007/3-540-68530-8_36

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64848-2

  • Online ISBN: 978-3-540-68530-2

  • eBook Packages: Springer Book Archive

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