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Signature Methods for the Assignment Problem

Author

Listed:
  • M. L. Balinski

    (C.N.R.S., Laboratoire d'Econométrie de I'Ecole Polytechnique, Paris)

Abstract

The “signature” of a dual feasible basis of the assignment problem is an n -vector whose i th component is the number of nonbasic activities of type ( i , j ). This paper uses signatures to describe a method for finding optimal assignments that terminates in at most ( n − 1)( n − 2)/2 pivot steps and takes at most O ( n 3 ) work.

Suggested Citation

  • M. L. Balinski, 1985. "Signature Methods for the Assignment Problem," Operations Research, INFORMS, vol. 33(3), pages 527-536, June.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:3:p:527-536
    DOI: 10.1287/opre.33.3.527
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    Citations

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    Cited by:

    1. Konstantinos Paparrizos & Nikolaos Samaras & Angelo Sifaleras, 2015. "Exterior point simplex-type algorithms for linear and network optimization problems," Annals of Operations Research, Springer, vol. 229(1), pages 607-633, June.
    2. Manfred Padberg & Dimitris Alevras, 1994. "Order‐preserving assignments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 395-421, April.
    3. Jingqun Li & R. Tharmarasa & Daly Brown & Thia Kirubarajan & Krishna R. Pattipati, 2019. "A novel convex dual approach to three-dimensional assignment problem: theoretical analysis," Computational Optimization and Applications, Springer, vol. 74(2), pages 481-516, November.
    4. Pritibhushan Sinha, 2009. "Assignment problems with changeover cost," Annals of Operations Research, Springer, vol. 172(1), pages 447-457, November.
    5. Qin, Xiaolin & Tang, Juan & Feng, Yong & Bachmann, Bernhard & Fritzson, Peter, 2016. "Efficient index reduction algorithm for large scale systems of differential algebraic equations," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 10-22.
    6. Orlin, James B., 1953-. & Ahuja, Ravindra K., 1956-., 1988. "New scaling algorithms for the assignment and minimum cycle mean problems," Working papers 2019-88., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    7. Michael Z. Spivey & Warren B. Powell, 2004. "The Dynamic Assignment Problem," Transportation Science, INFORMS, vol. 38(4), pages 399-419, November.
    8. Fanrui Xie & Tao Wu & Canrong Zhang, 2019. "A Branch-and-Price Algorithm for the Integrated Berth Allocation and Quay Crane Assignment Problem," Transportation Science, INFORMS, vol. 53(5), pages 1427-1454, September.
    9. Jingqun Li & Thia Kirubarajan & R. Tharmarasa & Daly Brown & Krishna R. Pattipati, 2021. "A dual approach to multi-dimensional assignment problems," Journal of Global Optimization, Springer, vol. 81(3), pages 691-716, November.
    10. Andrei Nikolaev & Anna Kozlova, 2021. "Hamiltonian decomposition and verifying vertex adjacency in 1-skeleton of the traveling salesperson polytope by variable neighborhood search," Journal of Combinatorial Optimization, Springer, vol. 42(2), pages 212-230, August.
    11. Ivan Belik & Kurt Jornsten, 2018. "Critical objective function values in linear sum assignment problems," Journal of Combinatorial Optimization, Springer, vol. 35(3), pages 842-852, April.
    12. Andrei V. Nikolaev & Egor V. Klimov, 2024. "Finding a second Hamiltonian decomposition of a 4-regular multigraph by integer linear programming," Journal of Combinatorial Optimization, Springer, vol. 47(5), pages 1-31, July.
    13. Chen, Liang & Tokuda, Naoyuki, 2001. "A faster data assignment algorithm for maximum likelihood-based multitarget motion tracking with bearings-only measurements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(1), pages 109-120.
    14. Ritter, Gunter & Pesch, Christoph, 2001. "Polarity-free automatic classification of chromosomes," Computational Statistics & Data Analysis, Elsevier, vol. 35(3), pages 351-372, January.

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