当前位置: X-MOL 学术Theor. Comput. Sci. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Computing a Longest Common Almost-Increasing Subsequence of Two Sequences
Theoretical Computer Science ( IF 0.9 ) Pub Date : 2020-11-20 , DOI: 10.1016/j.tcs.2020.11.035
Toan Thang Ta , Yi-Kung Shieh , Chin Lung Lu

Given a positive constant c, a sequence S=s1,s2,,sk of k numbers is said to be almost increasing if and only if si>max1j<isjc for all 1<ik. A longest common almost-increasing subsequence (LCaIS) between two input sequences is a longest common subsequence that is also an almost increasing sequence. We found out that the existing algorithm proposed by Moosa et al. [1] to find an LCaIS of two sequences without repeated elements gives an incorrect result for some instances. In this work, we present a dynamic programming algorithm that can correctly compute an LCaIS between any two sequences with repeated elements in O(nml) time and O(nm) space, where n and m are the lengths of two input sequences and l is the length of the output LCaIS.



中文翻译:

计算两个序列的最长公共几乎递增子序列

给定一个正常数c,一个序列小号=s1个s2sķ当且仅当k个数的k几乎增加s一世>最高1个Ĵ<一世sĴ-C 对所有人 1个<一世ķ。两个输入序列之间的最长公共几乎增加子序列(LCaIS)是最长公共子序列,它也是几乎增加的序列。我们发现Moosa等人提出的现有算法。文献[1]发现两个序列的LCaIS没有重复的元素在某些情况下给出了错误的结果。在这项工作中,我们提出了一种动态编程算法,该算法可以正确计算任意两个具有重复元素的序列之间的LCaISØñ 时间和 Øñ空间,其中nm是两个输入序列的长度,l是输出LCaIS的长度。

更新日期:2020-11-21
down
wechat
bug