Faster space-efficient STR-IC-LCS computation
One of the most fundamental method for comparing two given strings A and B is the longest common subsequence (LCS), where the task is to find (the length) of an LCS of A and B. In this paper, we deal with the STR-IC-LCS1 problem which is one of the constrained LCS problems proposed by Chen and Chao...
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| Veröffentlicht in: | Theoretical computer science Jg. 1003; S. 114607 |
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01.07.2024
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| Abstract | One of the most fundamental method for comparing two given strings A and B is the longest common subsequence (LCS), where the task is to find (the length) of an LCS of A and B. In this paper, we deal with the STR-IC-LCS1 problem which is one of the constrained LCS problems proposed by Chen and Chao [J. Comb. Optim, 2011]. A string Z is said to be an STR-IC-LCS of three given strings A, B, and P, if Z is a longest string satisfying that (1) Z includes P as a substring and (2) Z is a common subsequence of A and B. We present three efficient algorithms for this problem: First, we begin with a space-efficient solution which computes the length of an STR-IC-LCS in O(n2) time and O((ℓ+1)(n−ℓ+1)) space, where ℓ is the length of an LCS of A and B of length n. When ℓ=O(1) or n−ℓ=O(1), then this algorithm uses only linear O(n) space. Second, we present a faster algorithm that works in O(nr/logr+n(n−ℓ+1)) time, where r is the length of P, while retaining the O((ℓ+1)(n−ℓ+1)) space efficiency. Third, we give an alternative algorithm that runs in O(nr/logr+n(n−ℓ′+1)) time with O((ℓ′+1)(n−ℓ′+1)) space, where ℓ′ denotes the STR-IC-LCS length for input strings A, B, and P. |
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| AbstractList | One of the most fundamental method for comparing two given strings A and B is the longest common subsequence (LCS), where the task is to find (the length) of an LCS of A and B. In this paper, we deal with the STR-IC-LCS1 problem which is one of the constrained LCS problems proposed by Chen and Chao [J. Comb. Optim, 2011]. A string Z is said to be an STR-IC-LCS of three given strings A, B, and P, if Z is a longest string satisfying that (1) Z includes P as a substring and (2) Z is a common subsequence of A and B. We present three efficient algorithms for this problem: First, we begin with a space-efficient solution which computes the length of an STR-IC-LCS in O(n2) time and O((ℓ+1)(n−ℓ+1)) space, where ℓ is the length of an LCS of A and B of length n. When ℓ=O(1) or n−ℓ=O(1), then this algorithm uses only linear O(n) space. Second, we present a faster algorithm that works in O(nr/logr+n(n−ℓ+1)) time, where r is the length of P, while retaining the O((ℓ+1)(n−ℓ+1)) space efficiency. Third, we give an alternative algorithm that runs in O(nr/logr+n(n−ℓ′+1)) time with O((ℓ′+1)(n−ℓ′+1)) space, where ℓ′ denotes the STR-IC-LCS length for input strings A, B, and P. |
| ArticleNumber | 114607 |
| Author | Yonemoto, Yuki Nakashima, Yuto Bannai, Hideo Inenaga, Shunsuke |
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| Cites_doi | 10.1016/j.tcs.2008.08.042 10.1016/j.ipl.2012.02.007 10.1016/0022-0000(80)90002-1 10.1016/j.ipl.2003.07.001 10.1007/s10878-009-9262-5 10.1016/j.ipl.2004.02.008 10.1145/321796.321811 10.1093/comjnl/bxu012 10.1007/BF00264437 10.1145/360825.360861 |
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| SubjectTerms | Constrained longest common subsequence Dynamic programming String algorithms |
| Title | Faster space-efficient STR-IC-LCS computation |
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