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Exploiting Database Management Systems and Treewidth for Counting

Published online by Cambridge University Press:  12 March 2021

JOHANNES K. FICHTE ,
MARKUS HECHER Open the ORCID record for MARKUS HECHER [Opens in a new window] ,
PATRICK THIER  and
STEFAN WOLTRAN Open the ORCID record for STEFAN WOLTRAN [Opens in a new window]
JOHANNES K. FICHTE
Affiliation:
UC Berkeley, Berkeley, CA, USA (e-mail: johannes.fichte@berkeley.edu)
MARKUS HECHER
Affiliation:
TU Wien, Vienna, Austria (e-mails: hecher@dbai.tuwien.ac.at, thier@dbai.tuwien.ac.at, woltran@dbai.tuwien.ac.at)
PATRICK THIER
Affiliation:
TU Wien, Vienna, Austria (e-mails: hecher@dbai.tuwien.ac.at, thier@dbai.tuwien.ac.at, woltran@dbai.tuwien.ac.at)
STEFAN WOLTRAN
Affiliation:
TU Wien, Vienna, Austria (e-mails: hecher@dbai.tuwien.ac.at, thier@dbai.tuwien.ac.at, woltran@dbai.tuwien.ac.at)
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Abstract

Bounded treewidth is one of the most cited combinatorial invariants in the literature. It was also applied for solving several counting problems efficiently. A canonical counting problem is #Sat, which asks to count the satisfying assignments of a Boolean formula. Recent work shows that benchmarking instances for #Sat often have reasonably small treewidth. This paper deals with counting problems for instances of small treewidth. We introduce a general framework to solve counting questions based on state-of-the-art database management systems (DBMSs). Our framework takes explicitly advantage of small treewidth by solving instances using dynamic programming (DP) on tree decompositions (TD). Therefore, we implement the concept of DP into a DBMS (PostgreSQL), since DP algorithms are already often given in terms of table manipulations in theory. This allows for elegant specifications of DP algorithms and the use of SQL to manipulate records and tables, which gives us a natural approach to bring DP algorithms into practice. To the best of our knowledge, we present the first approach to employ a DBMS for algorithms on TDs. A key advantage of our approach is that DBMSs naturally allow for dealing with huge tables with a limited amount of main memory (RAM).

Keywords

dynamic programmingparameterized algorithmicsbounded treewidthdatabase systemsSQLrelational algebracounting

Information

Type
Rapid Communication
Information
Theory and Practice of Logic Programming , Volume 22 , Issue 1 , January 2022 , pp. 128 - 157
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

*

This is an extended version of a paper (Fichte et al. 2020) that appeared in the Proceedings of the 22nd International Symposium on Practical Aspects of Declarative Languages (PADL’20).

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