### Abstract

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 x_{i}ne/y_{i} (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.

Original language | English |
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Title of host publication | Proceedings - 12th Annual IEEE Conference on Computational Complexity, CCC 1997 (Formerly |

Subtitle of host publication | Structure in Complexity Theory Conference) |

Publisher | IEEE Computer Society |

Pages | 247-259 |

Number of pages | 13 |

ISBN (Electronic) | 0818679077 |

DOIs | |

Publication status | Published - Jan 1 1997 |

Event | 12th Annual IEEE Conference on Computational Complexity, CCC 1997 - Ulm, Germany Duration: Jun 24 1997 → Jun 27 1997 |

### Other

Other | 12th Annual IEEE Conference on Computational Complexity, CCC 1997 |
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Country | Germany |

City | Ulm |

Period | 6/24/97 → 6/27/97 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Computational Mathematics

### Cite this

*Proceedings - 12th Annual IEEE Conference on Computational Complexity, CCC 1997 (Formerly: Structure in Complexity Theory Conference)*(pp. 247-259). [612320] IEEE Computer Society. https://doi.org/10.1109/CCC.1997.612320

**The communication complexity of the universal relation.** / Tardos, G.; Zwick, U.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 12th Annual IEEE Conference on Computational Complexity, CCC 1997 (Formerly: Structure in Complexity Theory Conference).*, 612320, IEEE Computer Society, pp. 247-259, 12th Annual IEEE Conference on Computational Complexity, CCC 1997, Ulm, Germany, 6/24/97. https://doi.org/10.1109/CCC.1997.612320

}

TY - GEN

T1 - The communication complexity of the universal relation

AU - Tardos, G.

AU - Zwick, U.

PY - 1997/1/1

Y1 - 1997/1/1

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

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

U2 - 10.1109/CCC.1997.612320

DO - 10.1109/CCC.1997.612320

M3 - Conference contribution

AN - SCOPUS:0040218055

SP - 247

EP - 259

BT - Proceedings - 12th Annual IEEE Conference on Computational Complexity, CCC 1997 (Formerly

PB - IEEE Computer Society

ER -