On sampling with Markov chains

Random Structures and Algorithms

Volumn 9, Issue 1, 1996, Pages 55-77

  Chung, F R K ^a   Graham, R L ^b   Yau, S T ^c  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b LUCENT TECHNOLOGIES   (United States)

^c HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21444457747     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2418(199608/09)9:1/2<55::AID-RSA4>3.0.CO;2-A     Document Type: Article

References (21)

1. D. Aldous, On the Markov-chain simulation method for uniform combinatorial simulation and simulated annealing, Probab. Eng. Info. Sci., 1, 33-46 (1987).
2. J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, Elsevier, Amsterdam, 1976.
3. F. R. K. Chung, Laplacians of graphs and Cheeger's inequalities, in Combinatorics, Paul Erdös is Eighty, Bolyai Society Math. Studies, Vol. 2, Budapest, 1996, pp. 157-172
4. F. R. K. Chung and S.-T. Yau, A Harnack inequality for homogeneous graphs and subgraphs, Commun. Anal. Geom., 2, 628-639 (1994).
5. F. R. K. Chung and S.-T. Yau, Eigenvalue inequalities for graphs and convex subgraphs, Commun. Anal. Geom., to appear.
6. P. Diaconis and A. Gangolli, Rectangular arrays with fixed margins, preprint.
7. P. Diaconis and L. Saloff-Coste, Random walk on contingency tables with fixed row and column sums, preprint.
8. P. Diaconis and B. Sturmfels, Algebraic algorithms for sampling from conditional distributions, Ann. Stat., to appear
9. P. Diaconis, R. L. Graham, and B. Sturmfels, Primitive partition identities, in Combinatorics, Paul Erdös is Eighty, Bolyai Society Math. Studies, Vol. 2, Budapest, 1996, pp. 173-192.
10. M. Dyer, A. Freeze, and R. Kannan, A random polynomial time algorithm for approximating the volume of convex bodies, Proc. 21st ACM Symp. on Theory of Computing, 1989, pp. 375-381.
11. M. Dyer, A. Freeze, R. Kannan, A. Kapour, L. Perkovic, and U. Vazirani, A mildly exponential time algorithm for approximating the number of solutions to a multidimensional knapsack problem, Combinat. Probab. Comput., to appear.
12. M. Dyer, R. Kannan, and J. Mount, Sampling contingency tables, preprint.
13. P. Erdos and R. L. Graham, Old and new problems and results in combinatorial number theory, in L'Enseignement Mathematique, Mongographe No 28, Univ. of Genev̀e, Geneva, 1980, p. 86.
14. A. Frieze, R. Kannan and N. Polson, Sampling from log-concave distributions, Ann. Appl. Probab., 4, 812-837 (1994).
15. A. Gangolli, Convergence bounds for Markov chains and applications to sampling, Ph.D. dissertation, Dept. of Comput. Sci., Stanford University, 1991.
16. M. Jerrum and S. Sinclair, Fast uniform generation of regular graphs, Theor. Comput. Sci., 73, 91-100 (1990).
17. L. Lovász and M. Simonovits, The mixing rate of Markov chains, an isoperimetric inequality and computing the volume, Proc. 31st IEEE Symp. on Foundations of Computer Science, 1990, pp. 346-354.
18. B. McKay and N. Wormald, Uniform generation of random regular graphs of moderate degree, J. Alg., to appear.
19. R. Schoen and S-T. Yau, Differential Geometry, International Press, Cambridge, 1994.
20. A. Sinclair, Algorithms for Random Generation and Counting: A Markov Chain Approach, Birkhäuser, Boston, 1993.
21. A. Sinclair and M. Jerrum, Approximate counting, uniform generation and rapidly mixing Markov chains, Inf. Comput., 82, 93-133.