On the relative complexity of approximate counting problems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1913, Issue , 2000, Pages 108-119

  Dyer, Martin ^a   Goldberg, Leslie Ann ^b   Greenhill, Catherine ^c   Jerrum, Mark ^d  

^a UNIVERSITY OF LEEDS   (United Kingdom)

^b UNIVERSITY OF WARWICK   (United Kingdom)

^c UNIVERSITY OF MELBOURNE   (Australia)

^d UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMBINATORIAL MATHEMATICS; COMBINATORIAL OPTIMIZATION;

APPROXIMATE COUNTING; COUNTING PROBLEMS; EFFICIENT APPROXIMATION ALGORITHMS; INTERMEDIATE COMPLEXITY; RELATIVE COMPLEXITY; UNDER-APPROXIMATION;

APPROXIMATION ALGORITHMS;

EID: 84937395480     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44436-x_12     Document Type: Conference Paper

References (17)

1. G.R. Brightwell and P. Winkler, Graph homomorphisms and phase transitions, CDAM Research Report, LSE-CDAM-97-01, Centre for Discrete and Applicable Mathematics, London School of Economics, October 1997.
2. Martin Dyer, Leslie Ann Goldberg, Catherine Greenhill and Mark Jerrum, On the Relative Complexity of Approximate Counting Problems, Computer Science Research Report CS-RR-370, University of Warwick, February 2000. http://www.dcs.warwick.ac.uk/pub/index.html
3. M. Dyer, A. Frieze and M. Jerrum, On counting independent sets in sparse graphs, Proceedings of the 40th IEEE Symposium on Foundations of Computer Science (FOCS’99), IEEE Computer Society Press, 1999, 210–217.
4. M. Dyer and C. Greenhill, The complexity of counting graph homomorphisms (Extended abstract), Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’00), ACM-SIAM 2000, 246–255.
5. R. Fagin, Generalized first-order spectra and polynomial time recognisable sets. In “Complexity of Computation” (R. Karp, ed.), SIAM-AMS Proceedings 7, 1974, 43–73.
6. M. Jerrum and A. Sinclair, The Markov chain Monte Carlo method: an approach to approximate counting and integration. In Approximation Algorithms for NP-hard Problems (Dorit Hochbaum, ed.), PWS, 1996, 482–520.reducibility
7. M.R. Jerrum, L.G. Valiant and V.V. Vazirani, Random generation of combinatorial structures from a uniform distribution, Theoretical Computer Science 43 (1986), 169–188.
8. R.M. Karp, M. Luby and N. Madras, Monte-Carlo approximation algorithms for enumeration problems, Journal of Algorithms 10 (1989), 429–448.
9. P.W. Kasteleyn, Graph theory and crystal physics. In Graph Theory and Statistical Physics (F. Harary, ed.), Academic Press, 1967, 43–110.
10. J.S. Provan and M.O. Ball, The complexity of counting cuts and of computing the probability that a graph is connected, SIAM Journal on Computing 12 (1983), 777–788.
11. D. Roth, On the Hardness of approximate reasoning, Artificial Intelligence Journal 82 (1996), 273–302.
12. S. Saluja, K.V. Subrahmanyam and M.N. Thakur, Descriptive complexity of #P functions, Journal of Computer and Systems Sciences 50 (1995), 493–505.
13. J. Simon, On the difference between one and many (Preliminary version), Proceedings of the 4th International Colloquium on Automata, Languages and Programming (ICALP), Lecture Notes in Computer Science 52, Springer-Verlag, 1977, 480–491.
14. A. Sinclair, Algorithms for random generation and counting: a Markov chain approach, Progress in Theoretical Computer Science, Birkhäuser, Boston, 1993.
15. L. Stockmeyer, The complexity of approximate counting (preliminary version), Proceedings of the 15th ACM Symposium on Theory of Computing (STOC’83), ACM, 1983, 118–126.
16. S. Toda, PP is as hard as the polynomial-time hierarchy, SIAM Journal on Computing 20 (1991), 865–877.
17. L.G. Valiant and V.V. Vazirani, NP is as easy as detecting unique solutions, Theoretical Computer Science 47 (1986), 85–93.