Maximal common subsequence algorithms

Sakai, Yoshifumi

doi:10.1016/j.tcs.2019.06.020

Cited by 7 publications

(19 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When it is nonempty, we check for maximality of P for each of its elements (recalling |Ext P | = O(n)), which takes O(n) time by employing Sakai's maximality test [11]. If the test is positive, we only need to perform a leftward re-map of the new edge, which can be done in logarithmic time, totalizing O(|U| + |Ext P |(n + log n)) = O(n 2 ) time.…”

Section: Polynomial Delaymentioning

confidence: 99%

“…In general, LCSs only provide with information about the longest possible alignment between two strings, while MCSs offer a different range of information, possibly revealing slightly smaller but alternative alignments. A recent paper by Sakai [11] presents an algorithm that deterministically finds one MCS between two strings of length O(n) in O(n log log n) time, in contrast with the computation of the length of the LCS, for which a quadratic conditional lower bound based on SETH has been proved [1]. This same algorithm can also be used to extend a given sequence to a maximal one in the same time.…”

Section: Introductionmentioning

confidence: 99%

“…1. Lemma 1 (MCS Characterization [11]). Given a common subsequence W of X and Y , we define X k (resp.…”

Section: Introductionmentioning

confidence: 99%

“…As for the approach in [11], the algorithm cannot be easily generalized to solve Problem 1, since the specific choices it makes are crucial to ensure maximality of the output, and the direct iterated application of Lemma 1 does not lead to an efficient algorithm for Problem 1, as shown next.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Polynomial-Delay Enumeration of Maximal Common Subsequences

Conte

Grossi

Punzi

et al. 2019

String Processing and Information Retrieval

View full text Add to dashboard Cite

A Maximal Common Subsequence (MCS) between two strings X and Y is an inclusion-maximal subsequence of both X and Y. MCSs are a natural generalization of the classical concept of Longest Common Subsequence (LCS), which can be seen as a longest MCS. We study the problem of efficiently listing all the distinct MCSs between two strings. As discussed in the paper, this problem is algorithmically challenging as the same MCS cannot be listed multiple times: for example, dynamic programming [Fraser et al., CPM 1998] incurs in an exponential waste of time, and a recent algorithm for finding an MCS [Sakai, CPM 2018] does not seem to immediately extend to listing. We follow an alternative and novel graph-based approach, proposing the first output-sensitive algorithm for this problem: it takes polynomial time in n per MCS found, where n = max{|X|, |Y |}, with polynomial preprocessing time and space.

show abstract

Section: Polynomial Delaymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…1. Lemma 1 (MCS Characterization [11]). Given a common subsequence W of X and Y , we define X k (resp.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Polynomial-Delay Enumeration of Maximal Common Subsequences

Conte

Grossi

Punzi

et al. 2019

String Processing and Information Retrieval

View full text Add to dashboard Cite

show abstract

“…A dynamic programming approach is presented in [7] to find the shortest MCS. More recently, [17] proposes an computationally efficient way to find a MCS but his method can only find one MCS.…”

Section: Introductionmentioning

confidence: 99%

A Fast Randomized Algorithm for Finding the Maximal Common Subsequences

Cao,

Zhong

2020

Preprint

View full text Add to dashboard Cite

Finding the common subsequences of L multiple strings has many applications in the area of bioinformatics, computational linguistics, and information retrieval. A well known result states that finding a Longest Common Subsequence (LCS) for L strings is NP-hard, e.g., the computational complexity is exponential in L. In this paper, we develop a randomized algorithm, referred to as Random-MCS, for finding a random instance of Maximal Common Subsequence (MCS) of multiple strings. A common subsequence is maximal if inserting any character into the subsequence no longer yields a common subsequence. A special case of MCS is LCS where the length is the longest. We show the complexity of our algorithm is linear in L, and therefore is suitable for large L. Furthermore, we study the occurrence probability for a single instance of MCS, and demonstrate via both theoretical and experimental studies that the longest subsequence from multiple runs of Random-MCS often yields a solution to LCS.

show abstract

Enumeration of Maximal Common Subsequences Between Two Strings

et al. 2022

View full text Add to dashboard Cite

Maximal Common Subsequences (MCSs) between two strings X and Y are subsequences of both X and Y that are maximal under inclusion. MCSs relax and generalize the well known and widely used concept of Longest Common Subsequences (LCSs), which can be seen as MCSs of maximum length. While the number both LCSs and MCSs can be exponential in the length of the strings, LCSs have been long exploited for string and text analysis, as simple compact representations of all LCSs between two strings, built via dynamic programming or automata, have been known since the '70s. MCSs appear to have a more challenging structure: even listing them efficiently was an open problem open until recently, thus narrowing the complexity difference between the two problems, but the gap remained significant. In this paper we close the complexity gap: we show how to build DAG of polynomial size-in polynomial time-which allows for efficient operations on the set of all MCSs such as enumeration in Constant Amortized Time per solution (CAT), counting, and random access to the i-th element (i.e., rank and select operations). Other than improving known algorithmic results, this work paves the way for new sequence analysis methods based on MCSs.

show abstract

Maximal common subsequence algorithms

Cited by 7 publications

References 10 publications

Polynomial-Delay Enumeration of Maximal Common Subsequences

Polynomial-Delay Enumeration of Maximal Common Subsequences

A Fast Randomized Algorithm for Finding the Maximal Common Subsequences

Enumeration of Maximal Common Subsequences Between Two Strings

Contact Info

Product

Resources

About