分拣网络
分类
计算机科学
可满足性
解算器
构造(python库)
算法
理论计算机科学
排序算法
数学优化
数学
程序设计语言
作者
Daniel Bundala,Jakub Závodný
标识
DOI:10.1007/978-3-319-04921-2_19
摘要
This paper settles the optimality of sorting networks given in The Art of Computer Programming vol. 3 more than 40 years ago. The book lists efficient sorting networks with n ≤ 16 inputs. In this paper we give general combinatorial arguments showing that if a sorting network with a given depth exists then there exists one with a special form. We then construct propositional formulas whose satisfiability is necessary for the existence of such a network. Using a SAT solver we conclude that the listed networks have optimal depth. For n ≤ 10 inputs where optimality was known previously, our algorithm is four orders of magnitude faster than those in prior work.
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