Sparse Dynamic Programming I: Linear Cost Functions

Journal of the ACM (JACM)

Volumn 39, Issue 3, 1992, Pages 519-545

  Eppstein, David ^a   Galil, Zvi ^b   Giancarlo, Raffaele ^c   Italiano, Giuseppe F ^d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Och Spine at New York Presbyterian Hospitals   (United States)

^c LUCENT TECHNOLOGIES   (United States)

^d IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

dynamic programming; recurrence; sequence alignment; sparsity; time complexity

Indexed keywords

COMPUTATIONAL COMPLEXITY; DYNAMIC PROGRAMMING; NUMERICAL METHODS;

SPARSITY; TIME COMPLEXITY;

ALGORITHMS;

EID: 0026888975     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/146637.146650     Document Type: Article

References (29)

1. AGGARWAL, A., KLAWE, M. M., MORAN, S., SHOR, P., AND WILBER, R. Geometric applications of a matrix-searching algorithm.
2. AGGARWAL, A., AND PARK, J. Searching in multidimensional monotone matrices. In Proceedings of the 29th Annual Symposium on Foundations of Computer Science. IEEE, New York, 1988, pp. 497-512.
3. AHO, A. V., HOPCROFT, J. E., AND ULLMAN, J. D. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Mass., 1974.
4. AHO, A. V., HOPCROFT, J. E., AND ULLMAN, J. D Data structures and algorithms. Addison-Wesley, Reading, Mass., 1983.
5. APOSTOLICO, A., AND GUERRA, C. The longest common subsequence problem revisited Algorithmica 2 (1987), 315-336.
6. EPPSTEIN, D., GALIL, Z., AND GIANCARLO, R. Speeding up dynamic programming. In Proceedings of the 29th Symposium on the Foundations of Computer Science. IEEE, New York, 1988, pp. 488-496.
7. EPPSTEIN, D., GAUL, Z., GIANCARLO, R., AND ITALIANO, G. F. Sparse dynamic programming II: Convex and concave cost functions. J. ACM 39, 3 (July 1992), 546-567.
8. GALIL, Z., AND GIANCARLO, R. Speeding up dynamic programming with applications to molecular biology. Theoret. Comput. Sci. 64 (1989), 107-118.
9. JOHNSON, D. B. A priority queue in which initialization and queue operations take O(log log D) time. Math. Syst. Theory 15 (1982), 295-309.
10. HIRSCHBERG, D. S. Algorithms for the longest common subsequence problem. J. ACM 24. 4 (Oct. 1977), 664-675.
11. HIRSCHBERG, D. S., AND LARMORE, L. L. The least weight subsequence problem. SIAM J. Comput. 16 (1987), 628-638.
12. HUNT, J. W., AND SZYMANSKI, T. G. A fast algorithm for computing longest common subsequences. Commun. ACM 20, 5 (May 1977), 350-353.
13. KANEHISI, M. I., AND GOAD, W. B. Pattern recognition in Nucleic Acid Sequences II: An efficient method for finding locally stable secondary structures. Nuc. Acids Res. 10, 1 (1982), 265-277.
14. KLAWE, M. M., AND KLEITMAN, D. An almost linear algorithm for generalized matrix searching. SIAM J. Disc. Math. 3 (1990), 81-97.
15. KNUTH, D. E. The Art of Computer Programming, Volume 3: Sorting and Searching. Addison-Wesley, Reading, Mass., 1973.
16. LIPMAN, D. J., AND PEARSON, W. L. Rapid and Sensitive protein similarity searches. Science 2 (1985), 1435-1441.
17. MCCREIGHT, E. M. A space-economical suffix tree construction algorithm. J. ACM 23, 2 (Apr. 1976), 262-272.
18. MILLER, W., AND MYERS, E. W. Sequence comparison with concave weighting functions. Bull. Math. Biol. 50, 2 (1988), 97-120.
19. NEEDLEMAN, S. B., AND WUNSCH, C. D. A general method applicable to the search for similarities in the amino acid sequence of two proteins. J. Mol. Biol. 48 (1970), 443.
20. SANKOFF, D., KURSKAL, J. B., MAINVILLE, S., AND CEDERGREEN, R. J. Fast algorithms to determine RNA secondary structures containing multiple loops. In D. Sankoff and J. B. Kruskal, eds., Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison. Addison-Wesley, Reading, Mass., 1983. pp. 93-120.
21. TARJAN, R. E. Data Structures and Network Algorithms. SIAM, New York, 1985.
22. VAN EMDE BOAS, P. Preserving order in a forest in Less than logarithmic time. Inf. Proc. Lett. 6 (1977), 80-82.
23. WATERMAN, M. S., AND SMITH. T. F. RNA secondary structure: A complete mathematical analysis. Math. Biosci. 41 (1978), 257-266.
24. WATERMAN. M. S., AND SMITH, T. F. Rapid dynamic programming algorithms for RNA secondary structure. Adv. Appl. Math. 7 (1986), 455-464.
25. WATERMAN. M. S., SMITH, T. F., AND BEYER, W. A. Some biological sequence matrices. Adv. Math. 20 (1976), 367-387.
26. WEINER, P. Linear pattern matching algorithms. In Proceedings of the 14th Annual Symposium on Switching and Automata Theory. 1973, pp. 1-11.
27. WILBER, R. The concave least weight subsequence problem revisited. J. Algor. 9, 3 (1988), 418-425.
28. WILBUR, W. J., AND LIPMAN. D. J. Rapid similarity searches of nucleic acid and protein data banks. Proc. Nat. Acad. Sci. USA 80 (1983), 726-730.
29. WILBUR. W. J., AND LIPMAN, D. J. The context-dependent comparison of biological sequences. SIAM J. Appl. Math. 44, 3 (1984), 557-567.