Randomized Rounding for the Largest Simplex Problem

@article{Nikolov2015RandomizedRF,
  title={Randomized Rounding for the Largest Simplex Problem},
  author={Aleksandar Nikolov},
  journal={Proceedings of the forty-seventh annual ACM symposium on Theory of Computing},
  year={2015}
}
  • Aleksandar Nikolov
  • Published 28 November 2014
  • Mathematics, Computer Science
  • Proceedings of the forty-seventh annual ACM symposium on Theory of Computing
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… Expand
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