Solving convex programs by random walks
Journal of the ACM (JACM)
Dispersion of Mass and the Complexity of Randomized Geometric Algorithms
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Fast Algorithms for Logconcave Functions: Sampling, Rounding, Integration and Optimization
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Multi-dimensional online tracking
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Policy teaching through reward function learning
Proceedings of the 10th ACM conference on Electronic commerce
Complexity of Approximating the Vertex Centroid of a Polyhedron
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Monotonicity in bargaining networks
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A Randomized Cutting Plane Method with Probabilistic Geometric Convergence
SIAM Journal on Optimization
Complexity of approximating the vertex centroid of a polyhedron
Theoretical Computer Science
Multidimensional online tracking
ACM Transactions on Algorithms (TALG)
Software for exact integration of polynomials over polyhedra
Computational Geometry: Theory and Applications
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Consider the problem of computing the centroid of a convex body in n-dimensional Euclidean space. We prove that if the body is a polytope given as an intersection of half-spaces, then computing the centroid exactly is #P-hard, even for order polytopes, a special case of 0-1 polytopes. We also prove that if the body is given by a membership oracle, then for any deterministic algorithm that makes a polynomial number of queries there exists a body satisfying a roundedness condition such that the output of the algorithm is outside a ball of radius sigma/100 around the centroid, where sigma^2 is the minimum eigenvalue of the inertia matrix of the body.