From k-SAT to k-CSP: Two Generalized Algorithms

TL;DR

This paper extends two well-known algorithms, DPLL-like and PPSZ-like, from k-SAT to the more general k-CSP problems, marking the first such adaptation for the PPSZ-like approach.

Contribution

It introduces the first PPSZ-like algorithm for k-CSP and generalizes a DPLL-like algorithm, broadening the algorithmic toolkit for constraint satisfaction problems.

Findings

First PPSZ-like algorithm for k-CSP.

Generalization of DPLL-like algorithm to k-CSP.

Provides new strategies for solving NP-hard CSPs.

Abstract

Constraint satisfaction problems (CSPs) models many important intractable NP-hard problems such as propositional satisfiability problem (SAT). Algorithms with non-trivial upper bounds on running time for restricted SAT with bounded clause length k (k-SAT) can be classified into three styles: DPLL-like, PPSZ-like and Local Search, with local search algorithms having already been generalized to CSP with bounded constraint arity k (k-CSP). We generalize a DPLL-like algorithm in its simplest form and a PPSZ-like algorithm from k-SAT to k-CSP. As far as we know, this is the first attempt to use PPSZ-like strategy to solve k-CSP, and before little work has been focused on the DPLL-like or PPSZ-like strategies for k-CSP.