A Little Advice Can Be Very Helpful [chapter]

Arkadev Chattopadhyay, Jeff Edmonds, Faith Ellen, Toniann Pitassi
2012 Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms  
Proving superpolylogarithmic lower bounds for dynamic data structures has remained an open problem despite years of research. Recently, Pǎtraşcu proposed an exciting new approach for breaking this barrier via a two player communication model in which one player gets private advice at the beginning of the protocol. He gave reductions from the problem of solving an asymmetric version of set-disjointness in his model to a diverse collection of natural dynamic data structure problems in the cell
more » ... be model. He also conjectured that, for any hard problem in the standard two-party communication model, the asymmetric version of the problem is hard in his model, provided not too much advice is given. In this paper, we prove several surprising results about his model. We show that there exist Boolean functions requiring linear randomized communication complexity in the two-party model, for which the asymmetric versions in his model have deterministic protocols with exponentially smaller complexity. For setdisjointness, which also requires linear randomized communication complexity in the two-party model, we give a deterministic protocol for the asymmetric version in his model with a quadratic improvement in complexity. These results demonstrate that Pǎtraşcu's conjecture, as stated, is false. In addition, we show that the randomized and deterministic communication complexities of problems in his model differ by no more than a logarithmic multiplicative factor. We also prove lower bounds in some restricted versions of this model for natural functions such as setdisjointness and inner product. All of our upper bounds conform to these restrictions.
doi:10.1137/1.9781611973099.52 dblp:conf/soda/ChattopadhyayEEP12 fatcat:sz2qxfoiarcfrgnalz4ultiyd4