A decomposition theory for matroids. V. Testing of matrix total unimodularity
Journal of Combinatorial Theory Series B
Polynomial-time approximation algorithms for the Ising model
SIAM Journal on Computing
Splitting formulas for Tutte polynomials
Journal of Combinatorial Theory Series B
A Polynomial Time Algorithm to Find the Minimum Cycle Basis of a Regular Matroid
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Inapproximability of the Tutte polynomial
Information and Computation
Approximating the partition function of the ferromagnetic Potts model
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Approximate counting via correlation decay in spin systems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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We investigate the computational difficulty of approximating the partition function of the ferromagnetic Ising model on a regular matroid. Jerrum and Sinclair have shown that there is a fully polynomial randomised approximation scheme (FPRAS) for the class of graphic matroids. On the other hand, the authors have previously shown, subject to a complexity-theoretic assumption, that there is no FPRAS for the class of binary matroids, which is a proper superset of the class of graphic matroids. In order to map out the region where approximation is feasible, we focus on the class of regular matroids, an important class of matroids which properly includes the class of graphic matroids, and is properly included in the class of binary matroids. Using Seymour's decomposition theorem, we give an FPRAS for the class of regular matroids.