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Letter to the Editor—An Algorithm for Ranking all the Assignments in Order of Increasing Cost

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  • Katta G. Murty

    (University of California, Berkeley, California)

Abstract

The Hungarian method gives an efficient algorithm for finding the minimal cost assignment. However, in some cases it may be useful to determine the second minimal assignment (i.e., the best assignment after excluding the minimal cost assignment) and in general the k th minimal assignment for k = 1, 2, …. These things can easily be determined if all the assignments can be arranged as a sequence in increasing order of cost. This paper describes an efficient algorithm for such a ranking of all the assignments. The maximum computational effort required to generate an additional assignment in the sequence is that of solving at most ( n − 1) different assignment problems, one each of sizes 2, 3, …, n .

Suggested Citation

  • Katta G. Murty, 1968. "Letter to the Editor—An Algorithm for Ranking all the Assignments in Order of Increasing Cost," Operations Research, INFORMS, vol. 16(3), pages 682-687, June.
    • Handle: RePEc:inm:oropre:v:16:y:1968:i:3:p:682-687
    DOI: 10.1287/opre.16.3.682
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    Cited by:

    1. Christian Roed Pedersen & Lars Relund Nielsen & Kim Allan Andersen, 2008. "The Bicriterion Multimodal Assignment Problem: Introduction, Analysis, and Experimental Results," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 400-411, August.
    2. Kai Watermeyer & Jürgen Zimmermann, 2020. "A branch-and-bound procedure for the resource-constrained project scheduling problem with partially renewable resources and general temporal constraints," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 427-460, June.
    3. Gustavo Angulo & Shabbir Ahmed & Santanu S. Dey & Volker Kaibel, 2015. "Forbidden Vertices," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 350-360, February.
    4. Cowell, Robert G., 2013. "A simple greedy algorithm for reconstructing pedigrees," Theoretical Population Biology, Elsevier, vol. 83(C), pages 55-63.
    5. Molitor, P. & Jäger, G. & Goldengorin, B., 2005. "Some basics on tolerances," Research Report 05A13, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    6. Jamal Ouenniche & Prasanna K. Ramaswamy & Michel Gendreau, 2017. "A dual local search framework for combinatorial optimization problems with TSP application," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1377-1398, November.
    7. B. I. Goldengorin & D. S. Malyshev & P. M. Pardalos & V. A. Zamaraev, 2015. "A tolerance-based heuristic approach for the weighted independent set problem," Journal of Combinatorial Optimization, Springer, vol. 29(2), pages 433-450, February.

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