Abstract:
We consider worst case time bounds for NP-complete problems including 3-SAT, 3-coloring, 3-edge-coloring, and 3list -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. 1 Introduction There has recently been growing interest in analysis of superpolynomial-time algorithms, including algorithms for NP-hard problems such as satisfiability or graph coloring. This interest has multiple causes: . Many important applications can be modeled with these problems, and with the increased speed of modern computers, solved effectively; for instance it is now routine to solve hard 500-variable satisfia...
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