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Algorithms for counting 2SAT solutions and colorings with applications
 TR05033, Electronic Colloquium on Computational Complexity
, 2005
"... An algorithm is presented for exactly solving (in fact, counting) the number of maximum weight satisfying assignments of a 2Cnf formula. The worst case running time of ..."
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An algorithm is presented for exactly solving (in fact, counting) the number of maximum weight satisfying assignments of a 2Cnf formula. The worst case running time of
A Tighter Bound for Counting MaxWeight Solutions to 2SAT Instances
"... We give an algorithm for counting the number of maxweight solutions to a 2SAT formula, and improve the bound on its running time to O (1.2377 n). The main source of the improvement is a refinement of the method of analysis, where we extend the concept of compound (piecewise linear) measures to mult ..."
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We give an algorithm for counting the number of maxweight solutions to a 2SAT formula, and improve the bound on its running time to O (1.2377 n). The main source of the improvement is a refinement of the method of analysis, where we extend the concept of compound (piecewise linear) measures to multivariate measures, also allowing the optimal parameters for the measure to be found automatically. This method extension should be of independent interest.
Determining the number of solutions to binary CSP instances
"... Counting the number of solutions to CSP instances has applications in several areas, ranging from statistical physics to artificial intelligence. We give an algorithm for counting the number of solutions to binary CSPs, which works by transforming the problem into a number of 2sat instances, where ..."
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Counting the number of solutions to CSP instances has applications in several areas, ranging from statistical physics to artificial intelligence. We give an algorithm for counting the number of solutions to binary CSPs, which works by transforming the problem into a number of 2sat instances, where the total number of solutions to these instances is the same as those of the original problem. The algorithm consists of two main cases, depending on whether the domain size d is even, in which case the algorithm runs in O(1.3247 n · (d/2) n) time, or odd, in which case it runs in O(1.3247 n · ((d 2 + d + 2)/4) n/2) if d = 4 · k + 1, and O(1.3247 n · ((d 2 + d)/4) n/2) if d = 4 · k + 3. We also give an algorithm for counting the number of possible 3colourings of a given graph, which runs in O(1.8171 n), an improvement over our general algorithm gained by using problem specific knowledge.
Computing #2SAT of Grids, GridCylinders and GridTori Boolean Formulas
"... We present an adaptation of transfer matrix method for signed grids, gridcylinders and gridtori. We use this adaptation to count the number of satisfying assignments of Boolean Formulas in 2CNF whose corresponding associated graph has such grid topologies. 1 ..."
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We present an adaptation of transfer matrix method for signed grids, gridcylinders and gridtori. We use this adaptation to count the number of satisfying assignments of Boolean Formulas in 2CNF whose corresponding associated graph has such grid topologies. 1