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A New Algorithm for Computing the Maximal Closure of a Graph

Author

Listed:
  • Bruce Faaland

    (Graduate School of Business, University of Washington, Seattle, Washington 98195)

  • Kiseog Kim

    (Pusan National Unversity, Pusan, Republic of Korea)

  • Tom Schmitt

    (Graduate School of Business, University of Washington, Seattle, Washington 98195)

Abstract

A closure in a directed graph is a subset of nodes, all of whose successors belong to the subset. If each node has an assigned weight, which may be positive or negative, the maximal closure problem is one of finding a closure with the largest possible sum of node weights. It can be solved by any maximal flow or minimal cut algorithm. We present a new algorithm for this problem which compares favorably to maximal flow and minimal cut procedures on randomly generated classes of problems.

Suggested Citation

  • Bruce Faaland & Kiseog Kim & Tom Schmitt, 1990. "A New Algorithm for Computing the Maximal Closure of a Graph," Management Science, INFORMS, vol. 36(3), pages 315-331, March.
    • Handle: RePEc:inm:ormnsc:v:36:y:1990:i:3:p:315-331
    DOI: 10.1287/mnsc.36.3.315
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    Citations

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    Cited by:

    1. Prokic-Breuer, T. & Dronkers, J., 2012. "The high performance of Dutch and Flemish 15-year-old native pupils: explaining country differences in math scores between highly stratified educational systems," ROA Research Memorandum 008, Maastricht University, Research Centre for Education and the Labour Market (ROA).
    2. Csapó, Gergely & Müller, Rudolf, 2013. "Optimal mechanism design for the private supply of a public good," Games and Economic Behavior, Elsevier, vol. 80(C), pages 229-242.
    3. Zhi-Ming Chen & Cheng-Hsiung Lee & Hung-Lin Lai, 2022. "Speedup the optimization of maximal closure of a node-weighted directed acyclic graph," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1413-1437, December.
    4. M. Vanhoucke, 2006. "An efficient hybrid search algorithm for various optimization problems," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 06/365, Ghent University, Faculty of Economics and Business Administration.
    5. Thomas Schmitt & Bruce Faaland, 2004. "Scheduling recurrent construction," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(8), pages 1102-1128, December.

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