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Journal of the ACM (JACM)
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Discrete Mathematics
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SIAM Journal on Computing
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Worst-case upper bounds for MAX-2-SAT with an application to MAX-CUT
Discrete Applied Mathematics - The renesse issue on satisfiability
A new approach to proving upper bounds for MAX-2-SAT
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Counting models for 2SAT and 3SAT formulae
Theoretical Computer Science
New upper bounds for MAX-2-SAT and MAX-2-CSP w.r.t. the average variable degree
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Linear-programming design and analysis of fast algorithms for Max 2-CSP
Discrete Optimization
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Prior algorithms known for exactly solving Max 2-Satimprove upon the trivial upper bound only for very sparse instances. We present new algorithms for exactly solving (in fact, counting) weighted Max 2-Satinstances. One of them has a good performance if the underlying constraint graph has a small separator decomposition, another has a slightly improved worst case performance. For a 2-Satinstance Fwith nvariables, the worst case running time is $\tilde{O}(2^{(1-1/(\tilde{d}(F)-1))n})$, where $\tilde{d}(F)$ is the average degree in the constraint graph defined by F.We use strict 茂戮驴-gadgets introduced by Trevisan, Sorkin, Sudan, and Williamson to get the same upper bounds for problems like Max3-Satand Max Cut. We also introduce a notion of strict (茂戮驴,β)-gadget to provide a framework that allows composition of gadgets. This framework allows us to obtain the same upper bounds for Maxk-Satand Maxk-Lin-2.