Fast approximation of the permanent for very dense problems

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2008, Pages 681-689

  Huber, Mark ^a   Law, Jenny ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MARKOV CHAINS (MC); NONNEGATIVE ENTRIES; POLYNOMIAL-TIME; RUNNING TIME;

MARKOV PROCESSES;

POLYNOMIAL APPROXIMATION;

EID: 58449108073     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (27)

1. R. Ahuja, T. Magnanti, and J. Orlin, Network Flows, Prentice Hall, 1993.
2. A. Barvinok, Polynomial time algorithms to approximate permanents and mixed discriminants within a simply exponential factor, Random Structures Algorithms, 14 (1999), pp. 29-61.
3. I. Bezáková, D. Stefankovic, V. V. Vazirani, and E. Vigoda, Accelerating simulated annealing for the permanent and combinatorial counting problems, SODA '06: Proc. 17th ACM-SIAM Sympos. on Discrete Algorithms, 2006, pp. 900-907.
4. L. M. Bregman, Some properties of nonnegative matrices and their permanents, Soviet. Math. Dokl., 14 (1973), pp. 945-949.
5. A. Z. Broder, How hard is it to marry at random? (On the approximation of the permanent), STOC '86: Proc. 18th Annual ACM Sympos. on Theory of Computing, 1986, pp. 50-58.
6. P. Diaconis and D. Stroock, Geometric bounds for eigenvalues of Markov chains, Ann. Appl. Probab., 1 (1991), pp. 36-61.
7. B. Efron and V. Petrosian, Nonparametric Methods for Doubly Truncated Data, J. Amer. Statist. Assoc, 94 (1999), pp. 824-834.
8. G. P. Egorychev, The solution of van der Waerden's problem for pemanents, Advances in Math., 42 (1981), pp. 299-305.
9. D. I. Falikman, Proof of the van der Waerden's conjecture on the permanent of a doubly stochastic matrix, Mat. Zametki, 29 (1981), pp. 931-938.
10. G. S. Fishman, Choosing sample path length and number of sample paths when starting in the steady state, Oper. Res. Letters, 16 (1994), pp. 209-219.
11. 5/2 Algorithm for Maximum Matchings in Bipartite Graphs, SIAM J. Comput., 2 (1973), pp. 225-231.
12. M. Huber, Exact Sampling from Perfect Matchings of Dense Regular Bipartite Graphs, Algorithmica, 44 (2006), pp. 183-193.
13. M. Jerrum and A. Sinclair, Approximating the permanent, J. Comput., 18 (1989), pp. 1149-1178.
14. M. Jerrum and A. Sinclair, The Markov Chain Monte Carlo Method: An Approach to Approximate Counting and Integration, PWS Publishing, 1996.
15. M. Jerrum, L. Valiant, and V. Vazirani, Random generation of combinatorial structures from a uniform, distribution, Theoret. Comput. Sci., 43 (1986), pp. 169-188.
16. M. Jerrum and U. V. Vazirani, A Mildly Exponential Approximation Algorithm for the Permanent, Algorithmica, 16 (1996), pp. 392-401.
17. M. R. Jerrum, A. Sinclair, and E. Vigoda, A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries, J. of the ACM, 51 (2004), pp. 671-697.
18. B. Kalantari and L. Khachiyan, On the Complexity of Nonnegative-Matrix Scalings, Linear Algebra Appl., 240 (1996), pp. 87-103.
19. P. W. Kasteleyn, The statistics of dirners on a lattice, I., The number of dimer arrangements on a quadratic lattice, Physica, 27 (1961), pp. 1664-1672.
20. N. Linial, A. Samorodnitsky, and A. Wigderson, A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents, Combinatorica, 20 (2000), pp. 545-568.
21. J. H. Van Lint and R. M. Wilson, A Course in Combinatorics, Cambridge University Press, 1992.
22. H. Mine, Upper bounds for permanents of (0,1) - matrices, Bull. Amer. Math. Soc., 69 (1963), pp. 789-791.
23. R. Motwani and P. Raghavan, Randomized Algorithms, Cambridge University Press, 1995.
24. H. Pasula, S. J. Russell, M. Ostland, and Y. Ritov, Tracking many objects with many sensors, 16th Int. Joint Conf. on Artificial Intelligence (IJCAI), 1999, pp. 1160-1171.
25. R. Sinkhom, A relatiohship between arbitrary positive matrices and double stochastic matrices, A.. Math. Statist., 35 (1964), pp. 876-879.
26. G. W. Soules, Extending the Minc-Bregman upperbound for the permanent, Linear and Multilinear Algebra, 47 (2000), pp. 77-91.
27. L. G. Valiant, The complexity of computing the permanent, Theoret. Comput. Sci., 8 (1979), pp. 189-201.