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Efficient Algorithms for Consecutive Suffix Alignment via LCS Metric

This paper presents two novel algorithms addressing the Consecutive Suffix Alignment problem, a key variation of sequence similarity analysis. By exploring two strings, A and B, the goal is to compute the alignment solution for each suffix of A against B. The first algorithm operates in O(nL) time and space for constant alphabets, while the second extends to O(nL+n log |Σ|) time and O(L) space for general alphabets. These solutions enhance efficiency in incremental string comparisons, critical for applications in bioinformatics and pattern matching.

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Efficient Algorithms for Consecutive Suffix Alignment via LCS Metric

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  1. Two Algorithms for LCS Consecutive Suffix Alignment Gad M. Landau Eugene Myers and Michal Ziv-Ukelson CPM 2004 Presented by Jian-Fu Dong

  2. Abstract(1/2) • The problem of aligning two sequences A and B to determine their similarity is one of the fundamental problems in pattern matching. A challenging, basic variation of the sequence similarity problem is the incremental string comparison problem, denoted Consecutive Suffix Alignment, which is, given two string A and B, to compute the alignment solution of each suffix of A versus B.

  3. Abstract(2/2) Here, we present two solutions to the Consecutive Suffix Alignment Problem under the LCS metric. The first solution is an O(nL) time and space algorithm for constant alphabets, where n is the size of the compared strings and L<=n denotes the size of the LCS of A and B The second solution is an O(nL+nlog|Σ|) time and O(L) space algorithm for general alphabets, where Σ denotes the alphabet of the compared string

  4. Preliminaries-Problem Definition • Problem Definition : given two strings A and B, to compute the alignment solution of each suffix of A versus B

  5. Preliminaries-MatchList • MatchList(j) stores the list of indices of match points in column j of DP, sorted in increasing row index order

  6. Preliminaries-NextMatch • NextMatch(i,A[j]) denotes a function which returns the index of the next match point in column j of DP with row index greater than i, if such a match point exists. If no such match point exists, the function returns NULL

  7. Preliminaries-Partition Point • Pk denotes the set of partition points of DPk, where partition point Pkj [v] ,for k= 1…n, j= k…n, v = 0…Lk, denotes the first entry in column j of DPk which bears the value of v.

  8. First Algorithm

  9. Computing the New Partition Points of Column j of Pk(1/3)

  10. Computing the New Partition Points of Column j of Pk(2/3)

  11. Computing the New Partition Points of Column j of Pk(3/3)

  12. Time Complexity • Preprocessing stage : NextMatch table is construct in O(n|Σ|) time. • Updating P from Pn to P1 : O(n2)

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