Two algorithms for the longest common subsequence of three (or more) strings

Irving, Robert W.; Fraser, Campbell

doi:10.1007/3-540-56024-6_18

Cited by 46 publications

(33 citation statements)

References 11 publications

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“…This sheds a new light on the practicality of extending the algorithms by Miller and Myers as well as Wu et al for the k-LCS problem. Our results stand in contrast to the observations by Irving and Fraser in [12], and thus, we reopen the research in finding feasible optimal solutions to the k-LCS problem.…”

Section: Output: a Longest Common Subsequence (Lcs) Of The Input Stricontrasting

confidence: 99%

“…However, this improvement was by an order of magnitude less than our improvement over standard DP. Results for other degrees of similarity were not reported in [12]. Our experiments stand in contrast to the results reported in [12].…”

Section: Experimental Evaluationcontrasting

confidence: 99%

“…Notably, for 2-LCS the proposed algorithms by Miller and Myers [16] and its variant by Wu et al [25] have a favorable performance in the case of similar strings. We remark that the latter was extended for 3-LCS by Irving and Fraser in [12]. However, they experimentally found that their algorithm outperformed the standard dynamic programming only when |LCS| is very close to N (e.g.…”

Section: Output: a Longest Common Subsequence (Lcs) Of The Input Strimentioning

confidence: 99%

“…As mentioned before, [12] proposed another approach for extending W3M to 3D. The authors reported that standard DP outperformed W3M for problem instances where |LCS| was 50% of the input string length N .…”

Section: Experimental Evaluationmentioning

confidence: 99%

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Shortest Path Approaches for the Longest Common Subsequence of a Set of Strings

Barsky

Stege

Thomo

et al. 2007

2007 IEEE 7th International Symposium on BioInformatics and BioEngineering

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Abstract-We investigate the k-LCS problem that is finding a longest common subsequence (LCS) for k given input strings. The problem is known to have practical solutions for k = 2, but for higher dimensions it is not very well explored. We consider the algorithms by Miller and Myers as well as Wu et al. which solve the 2-LCS problem, and shed a new light on their generalization to higher dimensions. First, we redesign both algorithms such that the generalization to higher dimensions becomes natural. Then we present our algorithms for solving the k-LCS problem. We further propose a new approach to reduce the algorithms' space complexity. We demonstrate that our algorithms are practical as they significantly outperform the dynamic programming approaches. Our results stand in contrast to observations made in previous work by Irving and Fraser.

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Section: Output: a Longest Common Subsequence (Lcs) Of The Input Stricontrasting

confidence: 99%

Section: Experimental Evaluationcontrasting

confidence: 99%

Section: Output: a Longest Common Subsequence (Lcs) Of The Input Strimentioning

confidence: 99%

Section: Experimental Evaluationmentioning

confidence: 99%

See 2 more Smart Citations

Shortest Path Approaches for the Longest Common Subsequence of a Set of Strings

Barsky

Stege

Thomo

et al. 2007

2007 IEEE 7th International Symposium on BioInformatics and BioEngineering

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“…It measures the total length of the longest matching substrings in both texts, where these substrings are allowed to be noncontiguous as long as they appear in the same order [6,14]. While the original algorithm was applied to find substrings of characters, a natural extension is to consider it for words, i.e.…”

Section: Longest Common Subsequencementioning

confidence: 99%

Similarity-Based Support for Text Reuse in Technical Writing

Soto

Mohammad

Albert

et al. 2015

Proceedings of the 2015 ACM Symposium on Document Engineering

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Technical writing in professional environments, such as user manual authoring for new products, is a task that relies heavily on reuse of content. Therefore, technical content is typically created following a strategy where modular units of text have references to each other. One of the main challenges faced by technical authors is to avoid duplicating existing content, as this adds unnecessary effort, generates undesirable inconsistencies, and dramatically increases maintenance and translation costs. However, there are few computational tools available to support this activity. This paper investigates the use of different similarity methods for the task of identification of reuse opportunities in technical writing. We evaluated our results using existing ground truth as well as feedback from technical authors. Finally, we also propose a tool that combines text similarity algorithms with interactive visualizations to aid authors in understanding differences in a collection of topics and identifying reuse opportunities.

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Starting from Scratch: Growing Longest Common Subsequences with Evolution

Julstrom

Hinkemeyer

2006

Parallel Problem Solving From Nature - PPSN IX

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Two algorithms for the longest common subsequence of three (or more) strings

Cited by 46 publications

References 11 publications

Shortest Path Approaches for the Longest Common Subsequence of a Set of Strings

Shortest Path Approaches for the Longest Common Subsequence of a Set of Strings

Similarity-Based Support for Text Reuse in Technical Writing

Starting from Scratch: Growing Longest Common Subsequences with Evolution

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