arXiv 1509.010142015-09-03cs.DScs.CC

关于有界宽度问题的等价性

On the Equivalence among Problems of Bounded Width

Yoichi Iwata, Yuichi Yoshida

备注：: accepted to ESA 2015

摘要：

在本文中，我们介绍了一种方法，称为分解为基础的减少，显示各种问题之间的等价性的有界宽度。首先，我们证明了以下对于任何$α> 0$都是等价的：* SAT可以在$O^*(2^{α\mathrm{tw}})$时间内求解，* 3-SAT可以在$O^*(2^{α\mathrm{tw}})$时间内求解，* Max 2-SAT可以在$O^*(2^{α\mathrm{tw}})$时间内求解，* 独立集可以在$O^*(2^{α\mathrm{tw}})$时间内求解，* 独立集可以在$O^*(2^{α\mathrm{cw}})$时间内求解，其中tw和cw分别是实例的树宽和树宽。然后，我们引入了一个新的参数化复杂性类EPNL，它包含了集合覆盖和有向Hamilton性，并证明了SAT，3-SAT，Max 2-SAT和路径宽度参数化的独立集都是EPNL完备的.这意味着，如果这些EPNL完全问题之一可以在$O^*(c^k)$时间内解决，那么EPNL中的任何问题都可以在$O^*(c^k)$时间内解决。

英文摘要：

In this paper, we introduce a methodology, called decomposition-based reductions, for showing the equivalence among various problems of bounded-width. First, we show that the following are equivalent for any $α> 0$: * SAT can be solved in $O^*(2^{α\mathrm{tw}})$ time, * 3-SAT can be solved in $O^*(2^{α\mathrm{tw}})$ time, * Max 2-SAT can be solved in $O^*(2^{α\mathrm{tw}})$ time, * Independent Set can be solved in $O^*(2^{α\mathrm{tw}})$ time, and * Independent Set can be solved in $O^*(2^{α\mathrm{cw}})$ time, where tw and cw are the tree-width and clique-width of the instance, respectively. Then, we introduce a new parameterized complexity class EPNL, which includes Set Cover and Directed Hamiltonicity, and show that SAT, 3-SAT, Max 2-SAT, and Independent Set parameterized by path-width are EPNL-complete. This implies that if one of these EPNL-complete problems can be solved in $O^*(c^k)$ time, then any problem in EPNL can be solved in $O^*(c^k)$ time.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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