The cell probe complexity of dynamic data structures
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Private vs. common random bits in communication complexity
Information Processing Letters
An introduction to computational learning theory
An introduction to computational learning theory
On randomized one-round communication complexity
Computational Complexity
Lower Bounds for Dynamic Transitive Closure, Planar Point Location, and Parentheses Matching
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
New Lower Bound Techniques for Dynamic Partial Sums and Related Problems
SIAM Journal on Computing
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Limitations of learning via embeddings in euclidean half spaces
The Journal of Machine Learning Research
Towards proving strong direct product theorems
Computational Complexity
Logarithmic Lower Bounds in the Cell-Probe Model
SIAM Journal on Computing
Learning Complexity vs. Communication Complexity
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
A Direct Product Theorem for Discrepancy
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
On determinism versus non-determinism and related problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Complexity classes in communication complexity theory
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Communication Complexity Under Product and Nonproduct Distributions
Computational Complexity
A strong direct product theorem for disjointness
Proceedings of the forty-second ACM symposium on Theory of computing
Towards polynomial lower bounds for dynamic problems
Proceedings of the forty-second ACM symposium on Theory of computing
Unifying the Landscape of Cell-Probe Lower Bounds
SIAM Journal on Computing
| Hi-index | 0.00 |
Proving superpolylogarithmic lower bounds for dynamic data structures has remained an open problem despite years of research. Recently, Pătraşcu 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 probe 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 set-disjointness, 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 Pătraşcu'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 set-disjointness and inner product. All of our upper bounds conform to these restrictions.