# Algorithms for Variable-Weighted 2-SAT and Dual Problems

@inproceedings{Porschen2007AlgorithmsFV, title={Algorithms for Variable-Weighted 2-SAT and Dual Problems}, author={Stefan Porschen and Ewald Speckenmeyer}, booktitle={SAT}, year={2007} }

In this paper we study NP-hard variable-weighted satisfiability optimization problems for the class 2-CNF providing worst-case upper time bounds holding for arbitrary real-valued weights. Moreover, we consider the monotone dual class consisting of clause sets where all variables occur at most twice. We show that weighted SAT, XSAT and NAESAT optimization problems for this class are polynomial time solvable using appropriate reductions to specific polynomial time solvable graph problems.

## 8 Citations

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It is proved that XSAT remains NP-complete for linear formulas which are monotone and all variables occur exactly l times, and it is shown thatXSAT for this class is NP- complete, in contrast to SAT or NAE-SAT.

Parameterized and subexponential-time complexity of satisfiability problems and applications

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On Colored Edge Cuts in Graphs

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A symmetric model (SPED) that requires the two stubs of an edge to be of equal length, and an additional homogeneity constraint that forces the stub lengths to be a given fraction of the edge lengths ($\delta$-SHPED).

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An efficient solution for 2-planar drawings and a 2-approximation algorithm for the dual problem are presented and it is shown that, for a fixed stub---edge length ratio δ, not all graphs have a δ-SHPED.

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- Computer ScienceIEEE/ACM Transactions on Computational Biology and Bioinformatics
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A “progressive A*” search algorithm is developed using multiple heuristics, including the TBR and replug distances, to exactly compute the unrooted SPR distance, which is nearly two orders of magnitude faster than previous methods on small trees.

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