Improved algorithms for 3-coloring, 3-edge-coloring, and constraint satisfaction
David Eppstein · 2001
We consider worst case time bounds for NP-complete problems including 3-SAT, 3-coloring, 3-edgecoloring, 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.