Impatient PPSZ -- a Faster algorithm for CSP

TL;DR

This paper introduces 'impatient PPSZ', an improved version of the PPSZ algorithm for (d,k)-CSP problems, which sets variables more aggressively to achieve exponential performance gains for formulas with a unique solution.

Contribution

The paper proposes and analyzes 'impatient PPSZ', a modification that sets variables earlier when only two options remain, leading to exponential improvements over the original PPSZ.

Findings

Impatient PPSZ outperforms PPSZ exponentially for all k and d >= 3.

The modification is effective on formulas with a unique satisfying assignment.

The new algorithm maintains efficiency across a broad range of (d,k)-CSP problems.

Abstract

PPSZ is the fastest known algorithm for (d,k)-CSP problems, for most values of d and k. It goes through the variables in random order and sets each variable randomly to one of the d colors, excluding those colors that can be ruled out by looking at few constraints at a time. We propose and analyze a modification of PPSZ: whenever all but 2 colors can be ruled out for some variable, immediately set that variable randomly to one of the remaining colors. We show that our new "impatient PPSZ" outperforms PPSZ exponentially for all k and all d >= 3 on formulas with a unique satisfying assignment.