Random generation of combinatorial structures from a uniform
Theoretical Computer Science
Polynomial-time approximation algorithms for the Ising model
SIAM Journal on Computing
Complexity of generalized satisfiability counting problems
Information and Computation
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
Approximately counting up to four (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On Markov chains for independent sets
Journal of Algorithms
The complexity of counting graph homomorphisms
Proceedings of the ninth international conference on on Random structures and algorithms
On Markov chains for randomly H-coloring a graph
Journal of Algorithms
On Counting Independent Sets in Sparse Graphs
SIAM Journal on Computing
Very rapid mixing of the Glauber dynamics for proper colorings on bounded-degree graphs
Random Structures & Algorithms
Randomly coloring graphs of girth at least five
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Improved Bounds for Sampling Coloring
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Torpid Mixing of Some Monte Carlo Markov Chain Algorithms in Statistical Physics
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A Non-Markovian Coupling for Randomly Sampling Colorings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Counting and sampling H-colourings
Information and Computation
Slow mixing of Glauber dynamics for the hard-core model on the hypercube
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Torpid mixing of simulated tempering on the Potts model
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The Glauber Dynamics on Colorings of a Graph with High Girth and Maximum Degree
SIAM Journal on Computing
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
Randomly Coloring Constant Degree Graphs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Coupling with the stationary distribution and improved sampling for colorings and independent sets
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Counting independent sets up to the tree threshold
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The complexity of partition functions
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Randomly coloring sparse random graphs with fewer colors than the maximum degree
Random Structures & Algorithms
Towards a dichotomy theorem for the counting constraint satisfaction problem
Information and Computation
Simple deterministic approximation algorithms for counting matchings
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Randomly coloring planar graphs with fewer colors than the maximum degree
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Torpid mixing of local Markov chains on 3-colorings of the discrete torus
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Correlation decay and deterministic FPTAS for counting list-colorings of a graph
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Fast mixing for independent sets, colorings, and other models on trees
Random Structures & Algorithms
On counting homomorphisms to directed acyclic graphs
Journal of the ACM (JACM)
Path coupling using stopping times and counting independent sets and colorings in hypergraphs
Random Structures & Algorithms
The Complexity of the Counting Constraint Satisfaction Problem
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Random Structures & Algorithms
Holant problems and counting CSP
Proceedings of the forty-first annual ACM symposium on Theory of computing
The Complexity of Weighted Boolean CSP
SIAM Journal on Computing
An approximation trichotomy for Boolean #CSP
Journal of Computer and System Sciences
Proceedings of the forty-second ACM symposium on Theory of computing
The mixing time of Glauber dynamics for coloring regular trees
Random Structures & Algorithms
Graph homomorphisms with complex values: a dichotomy theorem
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Approximating the partition function of the ferromagnetic Potts model
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Computational Transition at the Uniqueness Threshold
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
A Decidable Dichotomy Theorem on Directed Graph Homomorphisms with Non-negative Weights
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
A very simple algorithm for estimating the number of k‐colorings of a low‐degree graph
Random Structures & Algorithms
A Complexity Dichotomy for Partition Functions with Mixed Signs
SIAM Journal on Computing
Non-negatively Weighted #CSP: An Effective Complexity Dichotomy
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Improved inapproximability results for counting independent sets in the hard-core model
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Guest column: complexity dichotomies of counting problems
ACM SIGACT News
Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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We give the first deterministic fully polynomial-time approximation scheme (FPTAS) for computing the partition function of a two-state spin system on an arbitrary graph, when the parameters of the system satisfy the uniqueness condition on infinite regular trees. This condition is of physical significance and is believed to be the right boundary between approximable and inapproximable. The FPTAS is based on the correlation decay technique introduced by Bandyopadhyay and Gamarnik [1] and Weitz [61]. The classic correlation decay is defined with respect to graph distance. Although this definition has natural physical meanings, it does not directly support an FPTAS for systems on arbitrary graphs, because for graphs with unbounded degrees, the local computation that provides a desirable precision by correlation decay may take super-polynomial time. We introduce a notion of computationally efficient correlation decay, in which the correlation decay is measured in a refined metric instead of graph distance. We use a potential method to analyze the amortized behavior of this correlation decay and establish a correlation decay that guarantees an inverse-polynomial precision by polynomial-time local computation. This gives us an FPTAS for spin systems on arbitrary graphs. This new notion of correlation decay properly reflects the algorithmic aspect of the spin systems, and may be used for designing FPTAS for other counting problems.