Asymptotic results for random multidimensional assignment problems

Computational Optimization and Applications

Volumn 31, Issue 3, 2005, Pages 275-293

  Grundel, Don ^a   Oliveira, Carlos A S ^b   Pardalos, Panos M ^b   Pasiliao, Eduardo ^a  

^a AIR FORCE RESEARCH LABORATORY   (United States)

^b University of Florida   (United States)

Author keywords

Asymptotic values; Combinatorial optimization; Multidimensional assignment

Indexed keywords

ASYMPTOTIC VALUES; COMBINATORIAL OPTIMIZATION; DATA ASSOCIATION; MULTIDIMENSIONAL ASSIGNMENT;

ASYMPTOTIC STABILITY; CONSTRAINT THEORY; COSTS; CURVE FITTING; DATA REDUCTION; OPTIMIZATION; RANDOM PROCESSES;

PROBLEM SOLVING;

EID: 23944519369     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-005-3227-0     Document Type: Article

References (23)

1. D. Aldous, quot;Asymptotics in the random assignment problem,quot; Probability Theory and Related Fields, vol. 93, pp. 507-534, 1992.
2. S.M. Andrijich and L. Caccetta, quot;Solving the multisensor data association problem,quot; Nonlinear Analysis, vol. 47, pp. 5525-5536, 2001.
3. D. Coppersmith and G. Sorkin, quot;Constructive bounds and exact expectations for the random assignment problem,quot; Random Structures and Algorithms, vol. 15, pp. 133-144, 1999.
4. D. Coppersmith and G. Sorkin, quot;On the expected incremental cost of a minimum assignment,quot; Technical Report, IBM T.J. Watson Research Center, 1999.
5. H. David, Order Statistics, John Wiley and Sons: New York, 1970.
6. Don Grundel, Carlos A.S. Oliveira, and Panos M. Pardalos, quot;Asymptotic properties of random multidimensional assignment problems,quot; Journal of Optimization Theory and Applications, vol. 122, no. 3, 2004.
7. Pierre Hansen and Nenad Mladenović, quot;Variable neighborhood search,quot; in Handbook of Applied Optimization, Panos M. Pardalos and Mauricio G. C. Resende, (Eds.), Oxford University Press: New York, NY, 2002, Chap. 3.6.9, pp. 221-234.
8. R.M. Karp, quot;An upper bound on the expected cost of an optimal assignment,quot; in Discrete Algorithms and Complexity: Proceedings of the Japan-US Joint Seminar, D. Johnson et al. (Eds.), Academic Press: New York, 1987, pp. 1-4.
9. T. Kirubarajan, Y. Bar-Shalom, and K.R. Pattipati, quot;Multiassignment for tracking a large number of overlapping objects,quot; IEEE Trans. Aerospace and Electronic Systems, vol. 37, no. 1, pp. 2-21, 2001.
10. A.M. Law and W.D. Kelton, Simulation Modeling and Analysis, 2nd edn., McGraw-Hill, Inc.: New York, 1991.
11. A.J. Lazarus, quot;The assignment problem with uniform (0,1) cost matrix,quot; Master's Thesis, Dept. of Mathematics, Princeton University, 1979.
12. S. Linusson and J. Wästlund, quot;A proof of Parisi's conjecture on the random assignment problem,quot; Available at http://www.mai.liu.se/jowas/,2003.
13. Mézard and Parisi, quot;Replicas and optimization,quot; J. Phys. Letters, vol. 46, pp. 771-778, 1985.
14. Mézard and Parisi, quot;On the solution of the random link matching problems,quot; J. Phys. Letters, vol. 48, pp. 1451-1459, 1987.
15. C. Nair, B. Prabhakar, and M. Sharma, quot;A proof of the conjecture due to parisi for the finite random assignment problem,quot; Available at http://www.stanford.edu/~balaji/rap.html, 2003.
16. B. Olin, quot;Asymptotic properties of random assignment problems,quot; PhD Thesis, Kungl Tekniska Högskolan, Stockholm, Sweden, 1992.
17. P.M. Pardalos and K.G. Ramakrishnan, quot;On the expected optimal value of random assignment problems: Experimental results and open questions,quot; Computational Optimization and Applications, vol. 2, pp. 261-271, 1993.
18. Eduardo L. Pasiliao, quot;Algorithms for multidimensional assignment problems,quot; PhD Thesis, Department of Industrial and Systems Engineering, University of Florida, Gainesville FL, 2003.
19. W.P. Pierskalla, quot;The multidimensional assignment problem,quot; Opera J., vol. 5, pp. 71-81, 1967.
20. A.B. Poore, N. Rijavec, M. Liggins, and V. Vannicola, quot;Data association problems posed as multidimensional assignment Problems: problem formulation,quot; in Signal and Data Processing of Small Targets, O.E. Drummond, (Ed.), SPIE: Bellingham, WA, 1993, pp. 552-561.
21. J. Pusztaszeri, P.E. Rensing, and T.M. Liebling, quot;Tracking elementary particles near their primary vertex: A combinatorial approach,quot; Journal of Global Optimization, vol. 9, no. 1, pp. 41-64, 1996.
22. W. Szpankowski, quot;Average case analysis of algorithms,quot; in Handbook of Algorithms and Theory of Computation, M. Atallah, (Ed.), CRC Press: Boca Raton, FL, 1998, pp. 14.1-14.38.
23. D.W. Walkup, quot;On the expected value of a random assignment problem,quot; SLAM Journal of Computing, vol. 8, pp. 440-442, 1979.