Random generation of combinatorial structures from a uniform
Theoretical Computer Science
Polynomial-time approximation algorithms for the Ising model
SIAM Journal on Computing
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
On Unapproximable Versions of NP-Complete Problems
SIAM Journal on Computing
What You Always Wanted to Know About Datalog (And Never Dared to Ask)
IEEE Transactions on Knowledge and Data Engineering
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
The Computational Complexity of Tutte Invariants for Planar Graphs
SIAM Journal on Computing
The phase transition in the cluster-scaled model of a random graph
Random Structures & Algorithms
The Complexity of Ferromagnetic Ising with Local Fields
Combinatorics, Probability and Computing
Inapproximability of the Tutte polynomial
Information and Computation
Journal of Combinatorial Theory Series B
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
Polynomial time randomized approximation schemes for Tutte–Gröthendieck invariants: The dense case
Random Structures & Algorithms
On the approximation complexity hierarchy
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
The complexity of approximately counting stable matchings
Theoretical Computer Science
The complexity of approximately counting stable matchings
Theoretical Computer Science
The expressibility of functions on the boolean domain, with applications to counting CSPs
Journal of the ACM (JACM)
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We provide evidence that it is computationally difficult to approximate the partition function of the ferromagnetic q-state Potts model when q 2. Specifically, we show that the partition function is hard for the complexity class #RHPi under approximation-preserving reducibility. Thus, it is as hard to approximate the partition function as it is to find approximate solutions to a wide range of counting problems, including that of determining the number of independent sets in a bipartite graph. Our proof exploits the first-order phase transition of the “random cluster” model, which is a probability distribution on graphs that is closely related to the q-state Potts model.