求最大汉明距离的快速指数时间算法X3SAT
A Fast Exponential Time Algorithm for Max Hamming Distance X3SAT
摘要：
X3 SAT是一个问题，是否可以满足一组给定的子句，其中最多有三个文字，使得在每个子句中，只有一个文字为真，其他文字为假。一个相关的问题是确定实例的两个解之间的最大汉明距离。Dahllöf提供了一个最大汉明距离XSAT的算法，它比X3 SAT的相同问题更复杂，运行时间为$O(1.8348^n)$ ; Fu，Zhou和Yin考虑了X3 SAT的最大汉明距离，并为这个问题找到了一个运行时间为$O(1.6760^n)$的算法。本文提出了一种在$O(1.3298^n)$时间内求解最大汉明距离X3 SAT问题的算法，该算法实际上是对每个$k$计算具有汉明距离$k$的解对的个数.
英文摘要：
X3SAT is the problem of whether one can satisfy a given set of clauses with up to three literals such that in every clause, exactly one literal is true and the others are false. A related question is to determine the maximal Hamming distance between two solutions of the instance. Dahllöf provided an algorithm for Maximum Hamming Distance XSAT, which is more complicated than the same problem for X3SAT, with a runtime of $O(1.8348^n)$; Fu, Zhou and Yin considered Maximum Hamming Distance for X3SAT and found for this problem an algorithm with runtime $O(1.6760^n)$. In this paper, we propose an algorithm in $O(1.3298^n)$ time to solve the Max Hamming Distance X3SAT problem; the algorithm actually counts for each $k$ the number of pairs of solutions which have Hamming Distance $k$.
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。
