Speeding Up Dynamic Programming without Omitting any Optimal Solution and Some Applications in Molecular Biology

We extend the algorithm of Galil and Giancarlo, which speeds up dynamic programming in the case of concave cost functions, such that a compact representation of all optimal solutions is computed. Compared to the Galil?Giancarlo algorithm our time bound grows only by a small constant factor. With a compact representation, we develop efficient algorithms for the solution of problems in molecular biology concerning the computation of all optimal local alignments and all optimal subalignments in genetic sequences.

[1]  Michael S. Waterman,et al.  General methods of sequence comparison , 1984 .

[2]  M. Waterman,et al.  A new algorithm for best subsequence alignments with application to tRNA-rRNA comparisons. , 1987, Journal of molecular biology.

[3]  M. Waterman.  Mathematical Methods for DNA Sequences , 1989 .

[4]  Daniel J. Kleitman,et al.  An Almost Linear Time Algorithm for Generalized Matrix Searching , 1990, SIAM J. Discret. Math..

[5]  Xiaoqiu Huang.  A Context Dependent Method for Comparing Sequences , 1994, CPM.

[6]  Robert E. Tarjan,et al.  A linear-time algorithm for a special case of disjoint set union , 1983, J. Comput. Syst. Sci..

[7]  Norbert Blum.  On Locally Optimal Alignments in Genetic Sequences , 1992, STACS.

[8]  S. Altschul,et al.  Optimal sequence alignment using affine gap costs. , 1986, Bulletin of mathematical biology.

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

[10]  P. Sellers.  On the Theory and Computation of Evolutionary Distances , 1974 .

[11]  O. Gotoh,et al.  Optimal sequence alignment allowing for long gaps. , 1990, Bulletin of mathematical biology.

[12]  O. Gotoh.  An improved algorithm for matching biological sequences. , 1982, Journal of molecular biology.

[13]  Dalit Naor,et al.  On Near-Optimal Alignments of Biological Sequences , 1994, J. Comput. Biol..

[14]  Peter H. Sellers,et al.  The Theory and Computation of Evolutionary Distances: Pattern Recognition , 1980, J. Algorithms.

[15]  Christus,et al.  A General Method Applicable to the Search for Similarities in the Amino Acid Sequence of Two Proteins , 2022 .

[16]  W. A. Beyer,et al.  Some Biological Sequence Metrics , 1976 .

[17]  M. I. Kanehisa,et al.  Pattern recognition in nucleic acid sequences. I. A general method for finding local homologies and symmetries , 1982, Nucleic Acids Res..

[18]  Robert E. Tarjan,et al.  Data structures and network algorithms , 1983, CBMS-NSF regional conference series in applied mathematics.

[19]  P. Sellers.  Pattern recognition in genetic sequences by mismatch density , 1984 .

[20]  Robert E. Tarjan,et al.  A Linear-Time Algorithm for a Special Case of Disjoint Set Union , 1985, J. Comput. Syst. Sci..

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

[22]  M S Waterman,et al.  Efficient sequence alignment algorithms. , 1984, Journal of theoretical biology.

[23]  M S Waterman,et al.  Identification of common molecular subsequences. , 1981, Journal of molecular biology.