3-Coloring in Time O(1.3289^n)
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; there is also a natural duality transformation from (a,b)-CSP to (b,a)-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.
Cite
@article{arxiv.cs/0006046,
title = {3-Coloring in Time O(1.3289^n)},
author = {Richard Beigel and David Eppstein},
journal= {arXiv preprint arXiv:cs/0006046},
year = {2010}
}
Comments
31 pages, 22 figures. An earlier version of this paper was presented at the 36th IEEE Symp. Foundations of Comp. Sci., 1995, and appears as ECCC TR 95-033