SAT中的 width-based algorithm

文献：

 
  
@inproceedings{DBLP:conf/sat/PipatsrisawatD09,
  author       = {Knot Pipatsrisawat and
                  Adnan Darwiche},
  editor       = {Oliver Kullmann},
  title        = {Width-Based Restart Policies for Clause-Learning Satisfiability Solvers},
  booktitle    = {Theory and Applications of Satisfiability Testing - {SAT} 2009, 12th
                  International Conference, {SAT} 2009, Swansea, UK, June 30 - July
                  3, 2009. Proceedings},
  series       = {Lecture Notes in Computer Science},
  volume       = {5584},
  pages        = {341--355},
  publisher    = {Springer},
  year         = {2009},
  url          = {https://doi.org/10.1007/978-3-642-02777-2\_32},
  doi          = {10.1007/978-3-642-02777-2\_32},
  timestamp    = {Tue, 14 May 2019 10:00:41 +0200},
  biburl       = {https://dblp.org/rec/conf/sat/PipatsrisawatD09.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}

 

 

重点内容在第2-3节

 

 

1. width-based algorithm

Galil [12] proposed a SAT algorithm which runs in time exponential in the width of the CNF formula. This algorithm, which was later reformulated in [13] and [9], works by deriving all resolvents of size ≤ k, for increasing k. Since there are only O(nk) clauses of size ≤ k,wheren is the total number of variables, this algorithm works well on formulas with bounded or small widths. Moreover, it was shown in [9] that this algorithm runs in time that is at most quasi-polynomial in the size of the smallest tree-like refutation proof (i.e., optimal DPLL). Nevertheless, one drawback which limits the practicality of this approach is the amount of memory it requires. Even though the space complexity of the algorithm is only exponential in the width of the proof, in practice, this could be a serious limiting factor–especially when compared to the clause-learning descendants of DPLL, which perform resolution in a more directed way and keep only a fraction of the resolvents in the knowledge base. The restart policies that we propose in this work can be thought of as a way to efficiently combine the benefits of both approaches. In other words, our approach canbeviewedasawayofusingthelowmemory requirement of modern clause learning SAT algorithms to loosely imitate the above width-based algorithm.

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2.   Existing and Width-Based Restart Policies

Width-Based Restart Policies for Clause-Learning Satisfiability Solvers. SAT 2009: 341-355

 

 
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