An algorithm is presented for exactly solving (in fact, counting) the number of maximum weight satisfying assignments of a 2-Cnf formula. The worst case running time of O(1.246) for formulas with n variables improves on the previous bound of O(1.256) by Dahllöf, Jonsson, and Wahlström. The algorithm uses only polynomial space. As a consequence we get an O(1.246) time algorithm for counting maxi...

The algorithm presented here, BCC, is an enhancement of the well known Backtrack used to solve constraint satisfaction problems. Though most backtrack improvements rely on propagation of local informations, BCC uses global knowledge of the constraint graph structure (and in particular its biconnected components) to reduce search space, permanently removing values and compiling partial solutions...

For a large number of random constraint satisfaction problems, such as random k-SAT and random graph and hypergraph coloring, we have very good estimates of the largest constraint density for which solutions exist. Yet, all known polynomial-time algorithms for these problems fail to find solutions even at much lower densities. To understand the origin of this gap one can study how the structure...