The distance approach to approximate combinatorial counting

Geometric and Functional Analysis

Volumn 11, Issue 5, 2001, Pages 871-899

  Barvinok, Alexander ^a   Samorodnitsky, Alex ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035563079     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-001-8219-3     Document Type: Article

References (17)

1. N. ALON, R. BOPPANA, J. SPENCER, An asymptotic isoperimetric inequality, Geom. Funct. Anal. 8 (1998), 411-436.
2. A. BARVINOK, Approximate counting via random optimization, Random Structures & Algorithms 11:2 (1997), 187-198.
3. M. GRÖTSCHEL, L. LOVÁSZ, A. SCHRIJVER, Geometric Algorithms and Combinatorial Optimization, second ed., Algorithms and Combinatorics, 2, Springer-Verlag, Berlin, 1993.
4. M. JERRUM, The computational complexity of counting, in "Proceedings of the International Congress of Mathematicians, Vol. 1,2 (Zürich, 1994)", Birkhäuser, Basel (1995), 1407-1416.
5. M. JERRUM, A. SINCLAIR, Approximating the permanent, SIAM J. Comput. 18:6 (1989), 1149-1178.
6. M. JERRUM, A. SINCLAIR, The Markov chain Monte Carlo method: an approach to approximate counting and integration, in "Approximation Algorithms for NP-hard Problems" D.S. Hochbaum, ed., PWS, Boston (1997), 483-520.
7. M. JERRUM, A. SINCLAIR, E. VIGODA, A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries, Electronic Colloquium on Computational Complexity, Report TR00-079, ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/2000/TR00-079/index.html
8. M. JERRUM, L.G. VALIANT, V.V. VAZIRANI, Random generation of combinatorial structures from a uniform distribution, Theoret. Comput. Sci., 43:2-3 (1986), 169-188.
9. I. LEADER, Discrete isoperimetric inequalities, in "Probabilistic Combinatorics and its Applications (San Francisco, CA, 1991)", Proc. Sympos. Appl. Math. 44, Amer. Math. Soc., Providence, RI (1991), 57-80.
10. J.H. VAN LINT, Introduction to Coding Theory, Third edition, Graduate Texts in Mathematics 86, Springer-Verlag, Berlin, 1999.
11. L. LOVÁSZ, M.D. PLUMMER, Matching Theory, North-Holland Mathematics Studies 121, Annals of Discrete Mathematics 29, North-Holland Publishing Co., Amsterdam-New York; Akadémiai Kiadó (Publishing House of the Hungarian Academy of Sciences), Budapest, 1986.
12. C. MCDIARMID, On the method of bounded differences, in "Surveys in Combinatorics 1989 (Norwich, 1989)", London Math. Soc. Lecture Note Ser. 141, Cambridge Univ. Press, Cambridge (1989), 148-188.
13. V.D. MILMAN, G. SCHECHTMAN, Asymptotic Theory of Finite-Dimensional Normed Spaces (with an Appendix by M. Gromov), Springer Lecture Notes in Mathematics 1200, 1986.
14. C.H. PAPADIMITRIOU, Computational Complexity, Addison-Wesley, Reading, Mass., 1994.
15. C.H. PAPADIMITRIOU, K. STEIGLITZ, Combinatorial Optimization: Algorithms and Complexity, Dover, NY, 1998.
16. E.M. RYCKMAN, Code for permanent approximations, experimental C++ code, available at http://www.math.lsa.umich.edu/~barvinok/papers.html
17. M. TALAGRAND, Concentration of measure and isoperimetric inequalities in product spaces, Inst. Hautes Études Sci. Publ. Math. 81 (1995), 73-205.