Nearly optimal separations between communication (or query) complexity and partitions

@article{Kothari2015NearlyOS,
  title={Nearly optimal separations between communication (or query) complexity and partitions},
  author={Robin Kothari},
  journal={Electron. Colloquium Comput. Complex.},
  year={2015},
  volume={22},
  pages={195}
}
  • Robin Kothari
  • Published 2015
  • Computer Science, Mathematics, Physics
  • Electron. Colloquium Comput. Complex.
We show a nearly quadratic separation between deterministic communication complexity and the logarithm of the partition number, which is essentially optimal. This improves upon a recent power 1.5 separation of Goos, Pitassi, and Watson (FOCS 2015). In query complexity, we establish a nearly quadratic separation between deterministic (and even randomized) query complexity and subcube partition complexity, which is also essentially optimal. We also establish a nearly power 1.5 separation between… Expand
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