Formula partitioning revisited

16 pages•Published: July 28, 2014

Abstract

Dividing a Boolean formula into smaller independent sub-formulae can be a useful technique for accelerating the solution of Boolean problems, including SAT and #SAT. Nevertheless, and despite promising early results, formula partitioning is hardly used in state-of-the-art solvers. In this paper, we show that this is rooted in a lack of consistency of the usefulness of formula partitioning techniques. In particular, we evaluate two existing and a novel partitioning model, coupled with two existing and two novel partitioning algorithms, on a wide range of benchmark instances. Our results show that there is no one-size-fits-all solution: for different formula types, different partitioning models and algorithms are the most suitable. While these results might seem negative, they help to improve our understanding about formula partitioning; moreover, the findings also give some guidance as to which method to use for what kinds of formulae.

Keyphrases: cnf partitioning, divide and conquer, fiduccia mattheyses algorithm, hypergraph partitioning, sat partitioning

In: Daniel Le Berre (editor). POS-14. Fifth Pragmatics of SAT workshop, vol 27, pages 41-56.

Links:	https://easychair.org/publications/paper/SD
	https://doi.org/10.29007/9skn