### Abstract

In this paper, we study the problem of computing the multiparty equality (MEQ) function: n≥2 nodes, each of which is given an input value from {1,⋯,K}, determine if their inputs are all identical, under the point-to-point communication model. The MEQ function equals to 1 if and only if all n inputs are identical, and 0 otherwise. The communication complexity of the MEQ problem is defined as the minimum number of bits communicated in the worst case. It is easy to show that (n-1)log_{2} K bits is an upper bound, by constructing a simple algorithm with that cost. In this paper, we demonstrate that communication cost strictly lower than this upper bound can be achieved. We show this by constructing a static protocol that solves the MEQ problem for n=3, K=6, of which the communication cost is strictly lower than the above upper bound (2log_{2} 6 bits). This result is then generalized for large values of n and K.

Original language | English (US) |
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Title of host publication | Structural Information and Communication Complexity - 18th International Colloquium, SIROCCO 2011, Proceedings |

Pages | 258-269 |

Number of pages | 12 |

DOIs | |

State | Published - Aug 10 2011 |

Event | 18th Colloquium on Structural Information and Communication Complexity, SIROCCO 2011 - Gdansk, Poland Duration: Jun 26 2011 → Jun 29 2011 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6796 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 18th Colloquium on Structural Information and Communication Complexity, SIROCCO 2011 |
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Country | Poland |

City | Gdansk |

Period | 6/26/11 → 6/29/11 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Structural Information and Communication Complexity - 18th International Colloquium, SIROCCO 2011, Proceedings*(pp. 258-269). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6796 LNCS). https://doi.org/10.1007/978-3-642-22212-2_23