An algorithm for solving linear programming programs in 0(n0S3L) operations
on Progress in Mathematical Programming: Interior-Point and Related Methods
On the complexity of approximating the maximal inscribed ellipsoid for a polytope
Mathematical Programming: Series A and B
Rounding of polytopes in the real number model of computation
Mathematics of Operations Research
Interior point algorithms: theory and analysis
Interior point algorithms: theory and analysis
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Projective clustering in high dimensions using core-sets
Proceedings of the eighteenth annual symposium on Computational geometry
Improved Complexity for Maximum Volume Inscribed Ellipsoids
SIAM Journal on Optimization
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On Numerical Solution of the Maximum Volume Ellipsoid Problem
SIAM Journal on Optimization
High-Dimensional Shape Fitting in Linear Time
Discrete & Computational Geometry
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In this paper, we consider the problem of computing a maximum inscribed sphere inside a high dimensional polytope formed by a set of halfspaces (or linear constraints) and with bounded aspect ratio, and present an efficient algorithm for computing a (1−ε)-approximation of the sphere. More specifically, given any aspect-ratio-bounded polytope P defined by n d-dimensional halfspaces, an interior point O of P, and a constant ε0, our algorithm computes in O(nd/ε3) time a sphere inside P with a radius no less than (1−ε)Ropt, where Ropt is the radius of a maximum inscribed sphere of P. Our algorithm is based on the core-set concept and a number of interesting geometric observations. Our result solves a special case of an open problem posted by Khachiyan and Todd [13].