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Log-Concave Polynomials IV: Approximate Exchange, Tight Mixing Times, and Near-Optimal Sampling of Forests
Nima Anari, Kuikui Liu, Shayan Oveis Gharan +2
We prove tight mixing time bounds for natural random walks on bases of matroids, determinantal distributions, and more generally distributions associated with log-concave polynomia…
Log-Concave Polynomials II: High-Dimensional Walks and an FPRAS for Counting Bases of a Matroid
Nima Anari, Kuikui Liu, Shayan Oveis Gharan +1
We design an FPRAS to count the number of bases of any matroid given by an independent set oracle, and to estimate the partition function of the random cluster model of any matroid…
Log-Concave Polynomials I: Entropy and a Deterministic Approximation Algorithm for Counting Bases of Matroids
Nima Anari, Shayan Oveis Gharan, Cynthia Vinzant
We give a deterministic polynomial time -approximation algorithm for the number of bases of a given matroid of rank and the number of common bases of any two matroids…