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- W2964269311 abstract "The maximum volume j-simplex problem asks to compute the j-dimensional simplex of maximum volume inside the convex hull of a given set of n points in Qd. We give a deterministic approximation algorithm for this problem which achieves an approximation ratio of ej/2 + o(j). The problem is known to be NP-hard to approximate within a factor of cj for some constant c > 1. Our algorithm also gives a factor ej + o(j) approximation for the problem of finding the principal j x j submatrix of a rank d positive semidefinite matrix with the largest determinant. We achieve our approximation by rounding solutions to a generalization of the D-optimal design problem, or, equivalently, the dual of an appropriate smallest enclosing ellipsoid problem. Our arguments give a short and simple proof of a restricted invertibility principle for determinants." @default.
- W2964269311 created "2019-07-30" @default.
- W2964269311 creator A5053901790 @default.
- W2964269311 date "2015-06-14" @default.
- W2964269311 modified "2023-09-24" @default.
- W2964269311 title "Randomized Rounding for the Largest Simplex Problem" @default.
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- W2964269311 doi "https://doi.org/10.1145/2746539.2746628" @default.
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