STOC '98 Proceedings of the thirtieth 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
Sharing one secret vs. sharing many secrets
Theoretical Computer Science - Mathematical foundations of computer science
Secure multiparty computation of approximations
ACM Transactions on Algorithms (TALG)
Sketching in adversarial environments
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Communication in the presence of replication
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Partition Arguments in Multiparty Communication Complexity
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
A direct sum theorem in communication complexity via message compression
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Parallel repetition of the odd cycle game
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
How to compress interactive communication
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
Partition arguments in multiparty communication complexity
Theoretical Computer Science
Strong direct product theorems for quantum communication and query complexity
Proceedings of the forty-third annual ACM symposium on Theory of computing
Interactive information complexity
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Sketching in Adversarial Environments
SIAM Journal on Computing
Resource-based corruptions and the combinatorics of hidden diversity
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Direct sum fails for zero error average communication
Proceedings of the 5th conference on Innovations in theoretical computer science
Multiparty communication complexity of vector---valued and sum---type functions
Information Theory, Combinatorics, and Search Theory
Choosing, Agreeing, and Eliminating in Communication Complexity
Computational Complexity
| Hi-index | 0.00 |
In this work we study the direct-sum problem with respect to communication complexity: Consider a relation $f$ defined over $\{0,1\}^{n} \times \{0,1\}^{n}$. Can the communication complexity of simultaneously computing $f$ on $\cal l$ instances $(x_1,y_1),\ldots,(x_{\cal l},y_{\cal l})$ be smaller than the communication complexity of computing $f$ on the $\cal l$ instances, separately? Let the amortized communication complexity of $f$ be the communication complexity of simultaneously computing $f$ on $\cal l$ instances, divided by $\cal l$. We study the properties of the amortized communication complexity. We show that the amortized communication complexity of a relation can be smaller than its communication complexity. More precisely, we present a partial function whose (deterministic) communication complexity is $\Theta(\log n)$ and its amortized (deterministic) communication complexity is $O(1)$. Similarly, for randomized protocols, we present a function whose randomized communication complexity is $\Theta(\log n)$ and its amortized randomized communication complexity is $O(1)$. We also give a general lower bound on the amortized communication complexity of any function $f$ in terms of its communication complexity $C(f)$: for every function $f$ the amortized communication complexity of $f$ is $\Omega \left (\sqrt{C(f)} - \log n \right)$.