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Graph Bisection Modeled As Cardinality Constrained Binary Quadratic Task Allocation

Author

Listed:
  • MARK LEWIS

    (Steven Craig School of Business, Missouri Western State University, Saint Joseph, MO, USA)

  • GARY KOCHENBERGER

    (School of Business, University of Colorado, Denver, CO, USA)

Abstract

In this paper, the cardinality constrained quadratic model for binary quadratic programming is used to model and solve the graph bisection problem as well as its generalization in the form of the task allocation problem with two processors (2-TAP). Balanced graph bisection is an NP-complete problem which partitions a set of nodes in the graphG = (N, E)into two sets with equal cardinality such that a minimal sum of edge weights exists between the nodes in the two separate sets. 2-TAP is graph bisection with the addition of node preference costs in the objective function. We transform the general linear k-TAP model to the cardinality constrained quadratic binary model so that it may be efficiently solved using tabu search with strategic oscillation. On a set of benchmark graph bisections, we improve the best known solution for several problems. Comparison results with the state-of-the-art graph partitioning program METIS, as well as Cplex and Gurobi are presented on a set of randomly generated graphs. This approach is shown to also work well with 2-TAP, comparing favorably to Cplex and Gurobi, providing better solutions in a much shorter time.

Suggested Citation

  • Mark Lewis & Gary Kochenberger, 2013. "Graph Bisection Modeled As Cardinality Constrained Binary Quadratic Task Allocation," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 261-276.
    • Handle: RePEc:wsi:ijitdm:v:12:y:2013:i:02:n:s0219622013500119
    DOI: 10.1142/S0219622013500119
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