## Abstract

We study the computation power of the congested clique, a model of distributed computation where n players communicate with each other over a complete network in order to compute some function of their inputs. The number of bits that can be sent on any edge in a round is bounded by a parameter b. We consider two versions of the model: in the first, the players communicate by unicast, allowing them to send a different message on each of their links in one round; in the second, the players communicate by broadcast, sending one message to all their neighbors. It is known that the unicast version of the model is quite powerful; to date, no lower bounds for this model are known. In this paper we provide a partial explanation by showing that the unicast congested clique can simulate powerful classes of bounded-depth circuits, implying that even slightly super-constant lower bounds for the congested clique would give new lower bounds in circuit complexity. Moreover, under a widely-believed conjecture on matrix multiplication, the triangle detection problem, studied in [8], can be solved in O(n^{ε}) time for any ε > 0. The broadcast version of the congested clique is the wellknown multi-party shared-blackboard model of communication complexity (with number-in-hand input). This version is more amenable to lower bounds, and in this paper we show that the subgraph detection problem studied in [8] requires polynomially many rounds for several classes of sub-graphs. We also give upper bounds for the subgraph detection problem, and relate the hardness of triangle detection in the broadcast congested clique to the communication complexity of set disjointness in the 3-party number-on-forehead model.

Original language | English |
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Title of host publication | PODC 2014 - Proceedings of the 2014 ACM Symposium on Principles of Distributed Computing |

Pages | 367-376 |

Number of pages | 10 |

DOIs | |

State | Published - 2014 |

Externally published | Yes |

Event | 2014 ACM Symposium on Principles of Distributed Computing, PODC 2014 - Paris, France Duration: 15 Jul 2014 → 18 Jul 2014 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Principles of Distributed Computing |
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### Conference

Conference | 2014 ACM Symposium on Principles of Distributed Computing, PODC 2014 |
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Country/Territory | France |

City | Paris |

Period | 15/07/14 → 18/07/14 |

## Keywords

- Congested clique
- Lower bounds
- Subgraph detection

## All Science Journal Classification (ASJC) codes

- Software
- Hardware and Architecture
- Computer Networks and Communications