The linear-array conjecture in communication complexity is false
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Amortizing randomness in private multiparty computations
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
Theoretical Computer Science
A new rank technique for formula size lower bounds
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A strong direct product theorem for disjointness
Proceedings of the forty-second ACM symposium on Theory of computing
Choosing, agreeing, and eliminating in communication complexity
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Breaking the rectangle bound barrier against formula size lower bounds
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
A stronger LP bound for formula size lower bounds via clique constraints
Theoretical Computer Science
Classical and quantum partition bound and detector inefficiency
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Choosing, Agreeing, and Eliminating in Communication Complexity
Computational Complexity
Hi-index | 0.00 |
It is possible to view communication complexity as the minimum solution of an integer programming problem. This integer programming problem is relaxed to a linear programming problem and from it information regarding the original communication complexity question is deduced. A particularly appealing avenue this opens is the possibility of proving lower bounds on the communication complexity (which is a minimization problem) by exhibiting upper bounds on the maximization problem defined by the dual of the linear program. This approach works very neatly in the case of nondeterministic communication complexity. In this case a special case of Lovasz's fractional cover measure is obtained. Through it the amortized nondeterministic communication complexity is completely characterized. The power of the approach is also illustrated by proving lower and upper bounds on the nondeterministic communication complexity of various functions. In the case of deterministic complexity the situation is more complicated. Two attempts are discussed and some results using each of them are obtained. The main result regarding the first attempt is negative: one cannot use this method for proving superpolynomial lower bounds for formula size. The main result regarding the second attempt is a "direct-sum" theorem for two-round communication complexity.