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Asymptotic Properties of Random Multidimensional Assignment Problem

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Encyclopedia of Optimization

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Article Outline

Keywords and Phrases

Introduction

Expected Optimal Value of Random MAP

Expected Number of Local Minima in Random MAP

  Local Minima and p-exchange Neighborhoods in MAP

  Expected Number of Local Minima in MAP with n = 2

  Expected Number of Local Minima in a~Random MAP with Normally Distributed Costs

Conclusions

References

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Notes

  1. 1.

    In the general case of MAP with \( { n_i } \) elements in dimension \( { i=1, \dots,d } \), the index graph would contain \( { n_1 } \) levels.

References

  1. Aiex RM, Resende MGC, Pardalos PM, Toraldo G (2005) GRASP with Path Relinking for Three-Index Assignment. INFORMS J Comput 17(2):224–247

    MathSciNet  Google Scholar 

  2. Aldous D (2001) The \( { \zeta(2) } \) limit in the random assignment problem. Random Struct Algorithm 18(4):381–418

    MathSciNet  MATH  Google Scholar 

  3. Alon N, Spencer J (2000) The Probabilistic Method, 2nd edn, Interscience Series in Discrete Mathematics and Optimization. Wiley, New York

    Google Scholar 

  4. Andrijich SM, Caccetta L (2001) Solving the multisensor data association problem. Nonlinear Analysis 47:5525–5536

    Google Scholar 

  5. Angel E, Zissimopoulos V (2001) On the landscape ruggedness of the quadratic assignment problem. Theor Comput Sci 263:159–172

    MathSciNet  MATH  Google Scholar 

  6. Balas E, Saltzman MJ (1991) An algorithm for the three-index assignment problem. Oper Res 39:150–161

    MathSciNet  MATH  Google Scholar 

  7. Burkard RE (2002) Selected topics on assignment problems. Discret Appl Math 123:257–302

    MathSciNet  MATH  Google Scholar 

  8. Garey MR, Johnson DS (1979) Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco

    MATH  Google Scholar 

  9. Goemans MX, Kodialam M (1993) A lower bound on the expected value of an optimal assignment. Math Oper Res 18:267–274

    MathSciNet  MATH  Google Scholar 

  10. Grundel DA, Oliveira CAS, Pardalos PM (2004) Asymptotic properties of random multidimensional assignment problems. J Optim Theory Appl 122(3):487–500

    MathSciNet  MATH  Google Scholar 

  11. Grundel DA, Krokhmal PA, Oliveira CAS, Pardalos PM (2007) Asymptotic properties of random multidimensional assignment problems. J Comb Optim 13(1):1–18

    MathSciNet  MATH  Google Scholar 

  12. Karp RM (1987) An upper bound on the expected cost of an optimal assignment. In: Discret Algorithm Complexity. Academic Press, Boston, pp 1–4

    Google Scholar 

  13. Krokhmal PA, Grundel DA, Pardalos P (2007) Asymptotic Behavior of the Expected Optimal Value of the Multidimensional Assignment Problem. Math Program 109(2–3):525–551

    Google Scholar 

  14. Lazarus AJ (1993) Certain expected values in the random assignment problem. Oper Res Lett 14:207–214

    MathSciNet  MATH  Google Scholar 

  15. Lin S, Kernighan BW (1973) An effective heuristic algorithm for the traveling salesman problem. Oper Res 21:498–516

    MathSciNet  MATH  Google Scholar 

  16. Linusson S, Wästlund J (2004) A proof of Parisi's conjecture on the random assignment problem. Probab Theory Relat Fields 128(3):419–440

    MATH  Google Scholar 

  17. Mézard M, Parisi G (1985) Replicas and optimization. J Phys Lett 46(17):771–778

    Google Scholar 

  18. Murphey R, Pardalos P, Pitsoulis L (1998) A greedy randomized adaptive search procedure for the multitarget multisensor tracking problem. In: DIMACS Series, vol 40, American Mathematical Society, pp 277–302

    Google Scholar 

  19. Nair C, Prabhakar B, Sharma M (2005) A Proof of the Conjecture due to Parisi for the Finite Random Assignment Problem. Random Struct Algorithms 27(4):413–444

    MathSciNet  MATH  Google Scholar 

  20. Olin B (1992) Asymptotic properties of the random assignment problem. Ph.D thesis, Royal Institute of Technology, Stockholm, Sweden

    Google Scholar 

  21. Palmer R (1991) Optimization on rugged landscapes. In: Perelson A, Kauffman S (eds) Molecular Evolution on Rugged Ladscapes: Proteins, RNA, and the Immune System. Addison Wesley, Redwood City, pp 3–25

    Google Scholar 

  22. Pardalos PM, Ramakrishnan KG (1993) On the expected optimal value of random assignment problems: Experimental results and open questions. Comput Optim Appl 2:261–271

    Google Scholar 

  23. Parisi G (1998) A conjecture on random bipartite matching. Physics e-Print archive, http://xxx.lang.gov/ps/cond-_mat/9801176

  24. Papadimitrou CH, Steiglitz K (1998) Combinatorial Optimization: Algorithms and Complexity. Dover, New York

    Google Scholar 

  25. Pasiliao EL (2003) Algorithms for Multidimensional Assignment Problems. PhD thesis, University of Florida

    Google Scholar 

  26. Pierskalla W (1968) The multidimensional assignment problem. Oper Res 16:422–431

    MATH  Google Scholar 

  27. Poore AB (1994) Multidimensional assignment formulation of data association problems arising from multitarget and multisensor tracking. Comput Optim Appl 3:27–54

    MathSciNet  MATH  Google Scholar 

  28. Pusztaszeri J, Rensing PE, Liebling TM (1995) Tracking elementary particles near their primary vertex: a combinatorial approach. J Glob Optim 16:422–431

    Google Scholar 

  29. Stanley R (1986) Enumerative Combinatorics. Wadsworth and Brooks, Belmont CA

    MATH  Google Scholar 

  30. Tong YL (1990) The Multivariate Normal Distribution. Springer, Berlin

    MATH  Google Scholar 

  31. Veenman CJ, Hendriks EA, Reinders MJT (1998) A fast and robust point tracking algorithm. Proc Fifth IEEE Int Conf Image Processing 653–657, Chicago, USA

    Google Scholar 

  32. Walkup DW (1979) On the expected value of a random assignment problem. SIAM J Comput 8:440–442

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, The University of Iowa, Iowa City, USA

    Pavlo A. Krokhmal

Authors
  1. Pavlo A. Krokhmal
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

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© 2008 Springer-Verlag

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Krokhmal, P.A. (2008). Asymptotic Properties of Random Multidimensional Assignment Problem . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_20

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