A direct proof for Lovett's bound on the communication complexity of low rank matrices
Computational Complexity
2014-09-24 v1 Discrete Mathematics
Abstract
The log-rank conjecture in communication complexity suggests that the deterministic communication complexity of any Boolean rank-r function is bounded by polylog(r). Recently, major progress was made by Lovett who proved that the communication complexity is bounded by O(r^1/2 * log r). Lovett's proof is based on known estimates on the discrepancy of low-rank matrices. We give a simple, direct proof based on a hyperplane rounding argument that in our opinion sheds more light on the reason why a root factor suffices and what is necessary to improve on this factor.
Keywords
Cite
@article{arxiv.1409.6366,
title = {A direct proof for Lovett's bound on the communication complexity of low rank matrices},
author = {Thomas Rothvoss},
journal= {arXiv preprint arXiv:1409.6366},
year = {2014}
}