Approximating the centroid is hard
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Enumerating contingency tables via random permanents
Combinatorics, Probability and Computing
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Adaptive simulated annealing: A near-optimal connection between sampling and counting
Journal of the ACM (JACM)
Random walks on polytopes and an affine interior point method for linear programming
Proceedings of the forty-first annual ACM symposium on Theory of computing
Large-scale uncertainty management systems: learning and exploiting your data
Proceedings of the 2009 ACM SIGMOD International Conference on Management of data
Sampling s-Concave Functions: The Limit of Convexity Based Isoperimetry
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Approximately Counting Integral Flows and Cell-Bounded Contingency Tables
SIAM Journal on Computing
The computational complexity of estimating MCMC convergence time
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On sampling from multivariate distributions
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Random Walks on Polytopes and an Affine Interior Point Method for Linear Programming
Mathematics of Operations Research
Optimization of a convex program with a polynomial perturbation
Operations Research Letters
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We prove that the hit-and-run random walk is rapidly mixing for an arbitrary logconcave distribution starting from any point in the support. This extends the work of [26], where this was shown for an important special case, and settles the main conjecture formulated there. From this result, we derive asymptotically faster algorithms in the general oracle model for sampling, rounding, integration and maximization of logconcave functions, improving or generalizing the main results of [24, 25, 1] and [16] respectively. The algorithms for integration and optimization both use sampling and are surprisingly similar.