关于GSAT的精度和运行时间
On the accuracy and running time of GSAT
摘要：
确定可满足性的随机算法被证明在解决具有数千个变量的问题时是有效的。然而，这些算法是不完整的。也就是说，它们不能保证一个令人满意的分配，如果存在的话，将被发现。因此，当研究随机算法，有两个重要的特性，需要考虑：运行时间，甚至更重要的是，精度--一个可能性的措施，一个令人满意的分配将被发现，如果一个存在。事实上，我们认为，如果没有提到的准确性，运行时间的概念，随机算法是不明确的。在本文中，我们引入了一个正式的概念的准确性。我们用它来定义运行时间的概念。我们使用这两个概念来研究随机游走策略GSAT算法。我们调查的准确性的输入公式，如子句变量比和满意的分配的数量的属性的依赖。我们证明了GSAT的运行时间呈指数增长的输入公式的变量的数量为随机生成的3-CNF公式和编码的3-和4-着色图的公式。
英文摘要：
Randomized algorithms for deciding satisfiability were shown to be effective in solving problems with thousands of variables. However, these algorithms are not complete. That is, they provide no guarantee that a satisfying assignment, if one exists, will be found. Thus, when studying randomized algorithms, there are two important characteristics that need to be considered: the running time and, even more importantly, the accuracy --- a measure of likelihood that a satisfying assignment will be found, provided one exists. In fact, we argue that without a reference to the accuracy, the notion of the running time for randomized algorithms is not well-defined. In this paper, we introduce a formal notion of accuracy. We use it to define a concept of the running time. We use both notions to study the random walk strategy GSAT algorithm. We investigate the dependence of accuracy on properties of input formulas such as clause-to-variable ratio and the number of satisfying assignments. We demonstrate that the running time of GSAT grows exponentially in the number of variables of the input formula for randomly generated 3-CNF formulas and for the formulas encoding 3- and 4-colorability of graphs.
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