Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Modified ranks of tensors and the size of circuits
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Amortized Communication Complexity
SIAM Journal on Computing
Communication complexity
Communications of the ACM
Distributed Source Coding Using Syndromes (DISCUS): Design and Construction
DCC '99 Proceedings of the Conference on Data Compression
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
A characterization of span program size and improved lower bounds for monotone span programs
Computational Complexity
Communication Complexity of Simultaneous Messages
SIAM Journal on Computing
Introduction to Coding Theory
Share conversion, pseudorandom secret-sharing and applications to secure computation
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Secure computation of constant-depth circuits with applications to database search problems
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
On the complexity of communication complexity
Proceedings of the forty-first annual ACM symposium on Theory of computing
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We consider the following problem. Suppose that a big amount of data is distributed among several parties, so that each party misses only few pieces of data. The parties wish to perform some global computation on the data while minimizing the communication between them. This situation is common in many real-life scenarios. A naive solution to this problem is to first perform a synchronization step, letting one party learn all pieces of data, and then let this party perform the required computation locally. We study the question of obtaining better solutions to the problem, focusing mainly on the case of computing low-degree polynomials via non-interactive protocols. We present interesting connections between this problem and the well studied cryptographic problem of secret sharing. We use this connection to obtain nontrivial upper bounds and lower bounds using results and techniques from the domain of secret sharing. The relation with open problems from the area of secret sharing also provides evidence for the difficulty of resolving some of the questions we leave open.