## Abstract

We prove tight network topology dependent bounds on the round complexity of computing well studied k-party functions such as set disjointness and element distinctness. Unlike the usual case in the CONGEST model in distributed computing, we x the function and then vary the underlying network topology. This complements the recent such results on total communication that have received some attention. We also present some applications to distributed graph computation problems. Our main contribution is a proof technique that allows us to reduce the problem on a general graph topology to a relevant two-party communication complexity problem. However, unlike many previous works that also used the same high level strategy, we do not reason about a two- party communication problem that is induced by a cut in the graph. To stitch' back the various lower bounds from the two party communication problems, we use the notion of timed graph that has seen prior use in network coding. Our reductions use some tools from Steiner tree packing and multi-commodity ow problems that have a delay constraint.

Original language | English |
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Title of host publication | 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 |

Editors | Philip N. Klein |

Publisher | Association for Computing Machinery |

Pages | 2524-2539 |

Number of pages | 16 |

ISBN (Electronic) | 9781611974782 |

DOIs | |

State | Published - 2017 |

Externally published | Yes |

Event | 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 - Barcelona, Spain Duration: 16 Jan 2017 → 19 Jan 2017 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | 0 |

### Conference

Conference | 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 |
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Country/Territory | Spain |

City | Barcelona |

Period | 16/01/17 → 19/01/17 |

### Bibliographical note

Publisher Copyright:Copyright © by SIAM.