Two Algorithms for LCS Consecutive Suffix Alignment

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 strings A and B, to compute the alignment solution of each suffix of A versus B.

[1]  David Eppstein,et al.  Sparse dynamic programming II: convex and concave cost functions , 1992, JACM.

[2]  Alberto Apostolico,et al.  The longest common subsequence problem revisited , 1987, Algorithmica.

[3]  David Eppstein,et al.  Sequence Comparison with Mixed Convex and Concave Costs , 1990, J. Algorithms.

[4]  David Eppstein,et al.  Speeding up dynamic programming , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[5]  Gad M. Landau,et al.  Incremental String Comparison , 1998, SIAM J. Comput..

[6]  Eugene W. Myers,et al.  AnO(ND) difference algorithm and its variations , 1986, Algorithmica.

[7]  Jeanette P. Schmidt,et al.  All Highest Scoring Paths in Weighted Grid Graphs and Their Application to Finding All Approximate Repeats in Strings , 1998, SIAM J. Comput..

[8]  Daniel S. Hirschberg,et al.  Algorithms for the Longest Common Subsequence Problem , 1977, JACM.

[9]  David Carmel,et al.  Searching XML documents via XML fragments , 2003, SIGIR.

[10]  Gad M. Landau,et al.  On the shared substring alignment problem , 2000, SODA '00.

[11]  Vladimir I. Levenshtein,et al.  Binary codes capable of correcting deletions, insertions, and reversals , 1965 .

[12]  Raffaele Giancarlo Dynamic programming: special cases , 1997, Pattern Matching Algorithms.

[13]  Sung-Ryul Kim,et al.  A Dynamic Edit Distance Table , 2000, CPM.

[14]  Alberto Apostolico,et al.  String Editing and Longest Common Subsequences , 1997, Handbook of Formal Languages.

[15]  Lawrence L. Larmore,et al.  The least weight subsequence problem , 1987, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[16]  Gad M. Landau,et al.  On the Common Substring Alignment Problem , 2001, J. Algorithms.

[17]  R. P. Dilworth,et al.  A DECOMPOSITION THEOREM FOR PARTIALLY ORDERED SETS , 1950 .

[18]  Gad M. Landau,et al.  An Extension of the Vector Space Model for Querying XML Documents via XML Fragments 1 , 2002 .

[19]  David Eppstein,et al.  Sparse dynamic programming I: linear cost functions , 1992, JACM.

[20]  Zvi Galil,et al.  A Linear-Time Algorithm for Concave One-Dimensional Dynamic Programming , 1990, Inf. Process. Lett..

[21]  E. Myers,et al.  Sequence comparison with concave weighting functions. , 1988, Bulletin of mathematical biology.

[22]  Gad M. Landau,et al.  A sub-quadratic sequence alignment algorithm for unrestricted cost matrices , 2002, SODA '02.

[23]  Alok Aggarwal,et al.  Geometric applications of a matrix-searching algorithm , 1987, SCG '86.

[24]  Gad M. Landau,et al.  Sparse LCS Common Substring Alignment , 2003, Inf. Process. Lett..

[25]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[26]  Raffaele Giancarlo,et al.  Speeding up Dynamic Programming with Applications to Molecular Biology , 1989, Theor. Comput. Sci..

[27]  Jeong Seop Sim,et al.  Approximate periods of strings , 2001, Theor. Comput. Sci..

[28]  Dan Gusfield,et al.  Algorithms on Strings, Trees, and Sequences - Computer Science and Computational Biology , 1997 .

[29]  Thomas G. Szymanski,et al.  A fast algorithm for computing longest common subsequences , 1977, CACM.

[30]  Alok Aggarwal,et al.  Notes on searching in multidimensional monotone arrays , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.