Fast and parallel decomposition of constraint satisfaction problems

Abstract

Constraint Satisfaction Problems (CSP) are notoriously hard. Consequently, powerful decomposition methods have been developed to overcome this complexity. However, this poses the challenge of actually computing such a decomposition for a given CSP instance, and previous algorithms have shown their limitations in doing so. In this paper, we present a number of key algorithmic improvements and parallelisation techniques to compute so-called Generalized Hypertree Decompositions (GHDs) faster. We thus advance the ability to compute optimal (i.e., minimal-width) GHDs for a significantly wider range of CSP instances on modern machines. This lays the foundation for more systems and applications in evaluating CSPs and related problems (such as Conjunctive Query answering) based on their structural properties.

Knowledge-Base Degrees of Inconsistency: Complexity and Counting

“…A further research direction is to study our algorithm for practical applications and stronger parameters, e.g., (Grohe and Marx 2014;Greco et al 2018), particularly, in the light of recent decomposition techniques (Gottlob, Okulmus, and Pichler 2020). Also enumeration complexity (Creignou et al 2017(Creignou et al , 2019Meier 2020) is worth studying in this context.…”