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
Polynomial time randomized approximation schemes for Tutte-Gro¨thendieck invariants: the dense case
Random Structures & Algorithms
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
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Rapid mixing of subset Glauber dynamics on graphs of bounded tree-width
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Approximate counting via correlation decay in spin systems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Approximating the partition function of the ferromagnetic Potts model
Journal of the ACM (JACM)
Approximating the Tutte polynomial of a binary matroid and other related combinatorial polynomials
Journal of Computer and System Sciences
| Hi-index | 0.00 |
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 #RHΠ1 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. A full version of this paper, with proofs included, is available at http://arxiv.org/abs/1002.0986.