## Abstract

In this paper, we prove topology dependent bounds on the number of rounds needed to compute Functional Aggregate Queries ($\FAQ$s) studied by Abo Khamis et al. [PODS 2016] in a synchronous distributed network under the model considered by Chattopadhyay et al. [FOCS 2014, SODA 2017]. Unlike the recent work on computing database queries in the Massively Parallel Computation model, in the model of Chattopadhyay et al., nodes can communicate only via private point-to-point channels and we are interested in bounds that work over an \em arbitrary communication topology. This model, which is closer to the well-studied $\congest$ model in distributed computing and generalizes Yao's two party communication complexity model, has so far only been studied for problems that are common in the two-party communication complexity literature. This is the first work to consider more practically motivated problems in this distributed model. For the sake of exposition, we focus on two specific problems in this paper: Boolean Conjunctive Query ($\BCQ$) and computing variable/factor marginals in Probabilistic Graphical Models (PGMs). We obtain tight bounds on the number of rounds needed to compute such queries as long as the underlying hypergraph of the query is $O(1)$-degenerate and has $O(1)$-arity. In particular, the $O(1)$-degeneracy condition covers most well-studied queries that are efficiently computable in the centralized computation model like queries with constant treewidth. These tight bounds depend on a new notion of 'width' (namely \em internal-node-width ) for Generalized Hypertree Decompositions (GHDs) of acyclic hypergraphs, which minimizes the number of internal nodes in a sub-class of GHDs. To the best of our knowledge, this width has not been studied explicitly in the theoretical database literature. Finally, we consider the problem of computing the product of a vector with a chain of matrices and prove tight bounds on its round complexity (over a finite field of two elements) using a novel min-entropy based argument.

Original language | English |
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Title of host publication | PODS 2019 - Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems |

Publisher | Association for Computing Machinery |

Pages | 432-449 |

Number of pages | 18 |

ISBN (Electronic) | 9781450362276 |

DOIs | |

State | Published - 13 Jun 2019 |

Externally published | Yes |

Event | 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems. PODS 2019, held in conjunction with the 2019 ACM SIGMOD International Conference on Management of Data, SIGMOD 2019 - Amsterdam, Netherlands Duration: 1 Jul 2019 → 3 Jul 2019 |

### Publication series

Name | Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems |
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### Conference

Conference | 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems. PODS 2019, held in conjunction with the 2019 ACM SIGMOD International Conference on Management of Data, SIGMOD 2019 |
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Country/Territory | Netherlands |

City | Amsterdam |

Period | 1/07/19 → 3/07/19 |

### Bibliographical note

Publisher Copyright:© 2019 ACM.

## Keywords

- Boolean conjunctive query
- Communication complexity lower bounds
- Congest model
- Probabalistic graphical models
- Topology dependent bounds