Improved Algorithms for 3-Coloring, 3-Edge-Coloring, and Constraint Satisfaction

TL;DR

This paper introduces improved algorithms for solving NP-complete problems like 3-coloring and 3-SAT by leveraging a CSP framework and combining backtracking with advanced matching and flow techniques.

Contribution

It presents a faster algorithm for (3,2)-CSP and applies it to enhance the worst-case time bounds for related problems such as 3-SAT and 3-coloring.

Findings

Faster algorithms for (3,2)-CSP.

Improved worst-case bounds for 3-coloring and 3-SAT.

Combination of backtracking with matching and flow methods.

Abstract

We consider worst case time bounds for NP-complete problems including 3-SAT, 3-coloring, 3-edge-coloring, and 3-list-coloring. Our algorithms are based on a constraint satisfaction (CSP) formulation of these problems; 3-SAT is equivalent to (2,3)-CSP while the other problems above are special cases of (3,2)-CSP. We give a fast algorithm for (3,2)-CSP and use it to improve the time bounds for solving the other problems listed above. Our techniques involve a mixture of Davis-Putnam-style backtracking with more sophisticated matching and network flow based ideas.