English

Fooling Polytopes

Computational Complexity 2018-08-14 v1 Combinatorics

Abstract

We give a pseudorandom generator that fools mm-facet polytopes over {0,1}n\{0,1\}^n with seed length polylog(m)logn\mathrm{polylog}(m) \cdot \log n. The previous best seed length had superlinear dependence on mm. An immediate consequence is a deterministic quasipolynomial time algorithm for approximating the number of solutions to any {0,1}\{0,1\}-integer program.

Keywords

Cite

@article{arxiv.1808.04035,
  title  = {Fooling Polytopes},
  author = {Ryan O'Donnell and Rocco A. Servedio and Li-Yang Tan},
  journal= {arXiv preprint arXiv:1808.04035},
  year   = {2018}
}