Abstract
Prior algorithms known for exactly solving Max 2-Sat improve upon the trivial upper bound only for very sparse instances. We present new algorithms for exactly solving (in fact, counting) weighted Max 2-Sat instances. 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-Sat instance F with n variables, 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 α-gadgets introduced by Trevisan, Sorkin, Sudan, and Williamson to get the same upper bounds for problems like Max 3-Sat and Max Cut. We also introduce a notion of strict (α,β)-gadget to provide a framework that allows composition of gadgets. This framework allows us to obtain the same upper bounds for Max k -Sat and Max k -Lin-2.
This material is based upon work supported by the National Science Foundation under Grant CCR-0209099.
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Fürer, M., Kasiviswanathan, S.P. (2007). Exact Max 2-Sat: Easier and Faster. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds) SOFSEM 2007: Theory and Practice of Computer Science. SOFSEM 2007. Lecture Notes in Computer Science, vol 4362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69507-3_22
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DOI: https://doi.org/10.1007/978-3-540-69507-3_22
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