Correlation decay and deterministic FPTAS for counting list-colorings of a graph

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn 07-09-January-2007, Issue , 2007, Pages 1245-1254

  Gamarnik, David ^a   Katz, Dmitriy ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; CONSTRAINT SATISFACTION PROBLEMS; GRAPH THEORY; MARKOV PROCESSES; POLYNOMIAL APPROXIMATION;

ARBITRARY CONSTANTS; ARBITRARY CONSTRAINTS; COMPUTATION TREES; COUNTING TECHNIQUES; DECAY OF CORRELATIONS; DETERMINISTIC ALGORITHMS; MARKOV CHAIN METHOD; STATISTICAL PHYSICS;

TREES (MATHEMATICS);

EID: 84969260612     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (17)

1. [BF87] I. Bárány and Z. Füredy, Computing the volume is difficult, Discrete Comput. Geom. 2 (1987), no. 4, 319-326.
2. [BG06] A. Bandyopadhyay and D. Gamarnik, Counting without sampling. New algorithms for enumeration problems using statistical physics., Proceedings of 17th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2006.
3. [BW02] G. Brightwell and P. Winkler, Random colorings of a Cayley tree, in Contemporary Combinatorics, B. Bollobas, ed., Bolyai Society Mathematical Studies, 2002, pp. 247-276.
4. [BW04] G.R. Brightwell and P. Winkler, Graph homomorphisms and long range action, in Graphs, morphisms and statistical physics (Nesetril and Winkler eds.), DIMACS series in discrete mathematics and computer science, 2004, pp. 29-47.
5. [DFHV04] M. Dyer, A. Frieze, T. Hayes, and E. Vigoda, Randomly coloring constant degree graphs, in Proceedings of 45th IEEE Symposium on Foundations of Computer Science, 2004.
6. [Ele86] G. Elekes, A geometric inequality and the complexity of computing volume, Discrete Comput. Geom. 1 (1986), no. 4, 289-292.
7. [FV06] A. Frieze and E. Vigoda, Survey of Markov chains for randomly sampling colorings, To appear in Festschrift for Dominic Welsh (2006).
8. [GMP05] L. A. Goldberg, R. Martin, and M. Paterson, Strong spatial mixing with fewer colors for lattice graphs, SIAM J. Comput. 35 (2005), no. 2, 486-517.
9. [Jer95] M. Jerrum, A very simple algorithm for estimating the number of k-colourings of a low-degree graph, Random Structures and Algorithms 7 (1995), no. 2, 157-165.
10. [Jon02] J. Jonasson, Uniqueness of uniform random colorings of regular trees, Statistics and Probability Letters 57 (2002), 243-248.
11. [JS06] K. Jung and D. Shah, On correctness of belief propagation algorithm, Preprint (2006).
12. [Sha05] D. Shah, Max weight independent set and matching via max-product, Preprint (2005).
13. [SS97] J. Salas and A. D. Sokal, Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem, J. Statist. Phys. 86 (1997), no. 3-4, 551-579.
14. [TJ02] S. Tatikonda and M. I. Jordan, Loopy belief propagation and gibbs measures, In Uncertainty in Artificial Intelligence (UAI), D. Koller and A. Darwiche (Eds)., 2002.
15. [Vig00] E. Vigoda, Improved bounds for sampling colorings, Journal of Mathematical Physics (2000).
16. [Wei05] D. Weitz, Counting down the tree, Submitted. (2005).
17. [YFW00] J. Yedidia, W. Freeman, and Y. Weiss, Understanding Belief Propagation and its generalizations, Mitsubishi Elect. Res. Lab. (2000), no. TR-2001-22.