A New Algorithm for Multi-objective Graph Partitioning⋆

  • Kirk Schloegel
  • George Karypis
  • Vipin Kumar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1685)


Recently, a number of graph partitioning applications have emerged with additional requirements that the traditional graph partitioning model alone cannot effectively handle. One such class of problems is those in which multiple objectives, each of which can be modeled as a sum of weights of the edges of a graph, must be simultaneously optimized. This class of problems can be solved utilizing a multi-objective graph partitioning algorithm. We present a new formulation of the multi-objective graph partitioning problem and describe an algorithm that computes partitionings with respect to this formulation. We explain how this algorithm provides the user with a fine-tuned control of the tradeoffs among the objectives, results in predictable partitionings, and is able to handle both similar and dissimilar objectives. We show that this algorithm is better able to find a good tradeoff among the objectives than partitioning with respect to a single objective only. Finally, we show that by modifying the input preference vector, the multi-objective graph partitioning algorithm is able to gracefully tradeoff decreases in one objective for increases in the others.


Single Objective Edge Weight Partitioning Problem Preference Vector Graph Partitioning Problem 
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  1. [1]
    P. Fishburn. Decision and Value Theory. J. Wiley & Sons, New York, 1964.Google Scholar
  2. [2]
    G. Karypis and V. Kumar. MeTiS: A software package for partitioning unstructured graphs, partitioning meshes, and computing_ll-reducing orderings of sparse matrices, version 4.0. 1998.Google Scholar
  3. [3]
    G. Karypis and V. Kumar. Multilevel algorithms for multi-constraint graph partitioning. Technical Report TR 98-019, Dept. of Computer Science, Univ. of Minnesota, 1998.Google Scholar
  4. [4]
    M. Makowski. Methodology and a modular tool for multiple criteria analysis of lp models. Technical Report WP-94-102, IIASA, 1994.Google Scholar
  5. [5]
    P. Yu. Multiple-Criteria Decision Making: Concepts, Techniques, and Extensions. Plenum Press, New York, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Kirk Schloegel
    • 1
  • George Karypis
    • 1
  • Vipin Kumar
    • 2
  1. 1.Department of Computer Science and EngineeringUniversity of MinnesotaMinnesotaUSA
  2. 2.Army HPC Research CenterMinneapolisUSA

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