61
Views
0
CrossRef citations to date
0
Altmetric
Section B

An algorithmic proof of Brégman–Minc theorem

, &
Pages 2181-2185 | Received 16 Aug 2008, Accepted 27 Aug 2008, Published online: 18 Mar 2009

References

  • Alon , N. , Spencer , J. H. and Erdos , P. 1992 . The Probabilistic Method , New York : Wiley .
  • Beichl , I. and Sullivan , F. 1999 . Approximating the permanent via importance sampling with application to the Dimer Covering Problem . J. Comput. Phys. , 149 : 128 – 147 .
  • Brégman , L. M. 1973 . Some properties of nonnegative matrices and their permanents . Soviet Math. Dok. , 14 : 945 – 949 .
  • Brualdi , R. A. and Ryser , H. J. 1991 . Combinatorial Matrix Theory , Cambridge : Cambridge University Press .
  • Friedland , S. , Rider , B. and Zeitouni , O. 2004 . Concentration of permanent estimators for certain large matrices . Ann. Appl. Probab. , 14 ( 3 ) : 1559 – 1576 .
  • Gutman , I. 1998 . Permanents of adjacency matrices and their dependence on molecular structure . Polycyclic Arom. Compd. , 12 : 281 – 287 .
  • Huo , Y. , Liang , H. , Liu , S. and Bai , F. 2008 . Computing monomer-dimer systems through matrix permanent . Phys. Rev. E , 77 ( 1 ) : 016706
  • Jerrum , M. , Sinclair , A. and Vigoda , E. 2004 . A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries . J. ACM , 51 ( 5 ) : 671 – 697 .
  • Karmarkar , N. , Karp , R. M. , Lipton , R. , Lovasz , L. and Luby , M. 1993 . A Monte Carlo algorithm for estimating the permanent . SIAM J. Comput. , 22 : 284 – 293 .
  • Liang , H. and Bai , F. 2004 . A new upper bound for permanent of (0,1)-matrices . Linear Algebra Appl. , 277 : 291 – 295 .
  • Linial , N. , Samorodnitsky , A. and Wigderson , A. 2000 . A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents . Combinatorica , 20 : 545 – 568 .
  • Minc , H. 1963 . Upper bound for permanents of (0,1)-matrices . Bull. Amer. Math. Soc. (N.S.) , 69 : 789 – 791 .
  • Minc , H. 1978 . Permanents , Reading, MA : Addison-Wesley .
  • Radhakrishnan , J. 1997 . An entropy proof of Brégman's theorem . J. Combin. Theory Ser. A , 77 : 161 – 164 .
  • Rasmussen , L. E. 1994 . Approximating the permanent: a simple approach . Random Structures Algorithms , 5 : 349 – 361 .
  • Schrijver , A. 1978 . A short proof of Minc's conjecture . J. Combin. Theory Ser. A , 25 : 80 – 83 .
  • Valliant , L. 1979 . The complexity of computing the permanent . Theoret. Comput. Sci. , 8 : 189 – 201 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.