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A Greedy Randomized Adaptive Search Procedure for the Feedback Vertex Set Problem

Author

Listed:
  • Panos M. Pardalos

    (University of Florida)

  • Tianbing Qian

    (The University of Iowa)

  • Mauricio G.C. Resende

    (AT&T Labs Research)

Abstract

A Greedy Randomized Adaptive Search Procedure (GRASP) is a randomized heuristic that has produced high quality solutions for a wide range of combinatorial optimization problems. The NP-complete Feedback Vertex Set (FVS) Problem is to find the minimum number of vertices that need to be removed from a directed graph so that the resulting graph has no directed cycle. The FVS problem has found applications in many fields, including VLSI design, program verification, and statistical inference. In this paper, we develop a GRASP for the FVS problem. We describe GRASP construction mechanisms and local search, as well as some efficient problem reduction techniques. We report computational experience on a set of test problems using three variants of GRASP.

Suggested Citation

  • Panos M. Pardalos & Tianbing Qian & Mauricio G.C. Resende, 1998. "A Greedy Randomized Adaptive Search Procedure for the Feedback Vertex Set Problem," Journal of Combinatorial Optimization, Springer, vol. 2(4), pages 399-412, December.
    • Handle: RePEc:spr:jcomop:v:2:y:1998:i:4:d:10.1023_a:1009736921890
    DOI: 10.1023/A:1009736921890
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    References listed on IDEAS

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    1. Manuel Laguna & Thomas A. Feo & Hal C. Elrod, 1994. "A Greedy Randomized Adaptive Search Procedure for the Two-Partition Problem," Operations Research, INFORMS, vol. 42(4), pages 677-687, August.
    2. Thomas A. Feo & Mauricio G. C. Resende & Stuart H. Smith, 1994. "A Greedy Randomized Adaptive Search Procedure for Maximum Independent Set," Operations Research, INFORMS, vol. 42(5), pages 860-878, October.
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