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SOFSEM
2007
Springer

Exact Max 2-Sat: Easier and Faster

10 years 5 months ago
Exact Max 2-Sat: Easier and Faster
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 ˜O(2(1−1/( ˜d(F )−1))n ), where ˜d(F) is the average degree in the constraint graph defined by F. The algorithms and bounds actually are valid for any Max 2-Csp, whose clauses are over pairs of binary variables. 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 ...
Martin Fürer, Shiva Prasad Kasiviswanathan
Added 09 Jun 2010
Updated 09 Jun 2010
Type Conference
Year 2007
Where SOFSEM
Authors Martin Fürer, Shiva Prasad Kasiviswanathan
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