An Efficient Dynamic Programming Algorithm for STR-IC-STR-IC-LCS Problem

In this paper, we consider a generalized longest common subsequence problem, in which a constraining sequence of length s must be included as a substring and the other constraining sequence of length t must be included as a subsequence of two main sequences and the length of the result must be maxim...

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Bibliographic Details
Published inAdvances in Knowledge Discovery and Data Mining pp. 466 - 477
Main Authors Zhu, Daxin, Wu, Yingjie, Wang, Xiaodong
Format Book Chapter
LanguageEnglish
Published Cham Springer International Publishing 2016
SeriesLecture Notes in Computer Science
Subjects
Dynamic programming
Longest common subsequence problem
Substring inclusion constraints
Time complexity
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ISBN3319317490
9783319317496
ISSN0302-9743
1611-3349
DOI10.1007/978-3-319-31750-2_37

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Summary:In this paper, we consider a generalized longest common subsequence problem, in which a constraining sequence of length s must be included as a substring and the other constraining sequence of length t must be included as a subsequence of two main sequences and the length of the result must be maximal. For the two input sequences X and Y of lengths n and m, and the given two constraining sequences of length s and t, we present an O(nmst) time dynamic programming algorithm for solving the new generalized longest common subsequence problem. The time complexity can be reduced further to cubic time in a more detailed analysis. The correctness of the new algorithm is proved.
ISBN:3319317490
9783319317496
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-319-31750-2_37