TY - GEN

T1 - The communication complexity of the universal relation

AU - Tardos, G.

AU - Zwick, U.

N1 - Publisher Copyright:
© 1997 IEEE.

PY - 1997

Y1 - 1997

N2 - Consider the following communication problem. Alice gets a word x∈{0,1}n and Bob gets a word y∈{0,1}n. Alice and Bob are told that xne/y. Their goal is to find an index 1les/iles/n such that xine/yi (the index i should be known to both of them). This problem is one of the most basic communication problems. It arises naturally from the correspondence between circuit depth and communication complexity discovered by M. Karchmer and A. Wigderson (1990). We present three protocols using which Alice and Bob can solve the problem by exchanging at most it n+2 bits. One of this protocols is due to S. Rudich and G. Tardos. These protocols improve the previous upper bound of n+log∗ n, obtained by M. Karchmer. We also show that any protocol for solving the problem must exchange, in the worst case, at least n+1 bits. This improves a simple lower bound of n-1 obtained by Karchmer. Our protocols, therefore, are at most one bit away from optimality.

AB - Consider the following communication problem. Alice gets a word x∈{0,1}n and Bob gets a word y∈{0,1}n. Alice and Bob are told that xne/y. Their goal is to find an index 1les/iles/n such that xine/yi (the index i should be known to both of them). This problem is one of the most basic communication problems. It arises naturally from the correspondence between circuit depth and communication complexity discovered by M. Karchmer and A. Wigderson (1990). We present three protocols using which Alice and Bob can solve the problem by exchanging at most it n+2 bits. One of this protocols is due to S. Rudich and G. Tardos. These protocols improve the previous upper bound of n+log∗ n, obtained by M. Karchmer. We also show that any protocol for solving the problem must exchange, in the worst case, at least n+1 bits. This improves a simple lower bound of n-1 obtained by Karchmer. Our protocols, therefore, are at most one bit away from optimality.

UR - http://www.scopus.com/inward/record.url?scp=0040218055&partnerID=8YFLogxK

U2 - 10.1109/CCC.1997.612320

DO - 10.1109/CCC.1997.612320

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AN - SCOPUS:0040218055

T3 - Proceedings of the Annual IEEE Conference on Computational Complexity

SP - 247

EP - 259

BT - Proceedings - 12th Annual IEEE Conference on Computational Complexity, CCC 1997 (Formerly: Structure in Complexity Theory Conference)

PB - IEEE Computer Society

T2 - 12th Annual IEEE Conference on Computational Complexity, CCC 1997

Y2 - 24 June 1997 through 27 June 1997

ER -