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Exploiting Database Management Systems and Treewidth for Counting

Published online by Cambridge University Press:  12 March 2021

JOHANNES K. FICHTE
Affiliation:
UC Berkeley, Berkeley, CA, USA (e-mail: [email protected])
MARKUS HECHER
Affiliation:
TU Wien, Vienna, Austria (e-mails: [email protected], [email protected], [email protected])
PATRICK THIER
Affiliation:
TU Wien, Vienna, Austria (e-mails: [email protected], [email protected], [email protected])
STEFAN WOLTRAN
Affiliation:
TU Wien, Vienna, Austria (e-mails: [email protected], [email protected], [email protected])

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).

Type
Rapid Communication
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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