The shortest common superstring problem: average case analysis for both exact and approximate matching

IEEE Transactions on Information Theory

Volumn 45, Issue 6, 1999, Pages 1867-1886

  Yang, En Hui ^a   Zhang, Zhen ^b  

^a UNIVERSITY OF WATERLOO   (Canada)

^b University of Southern California   (United States)

Author keywords

Data compression; Dna sequencing; Lower mutual information; Shortest common superstring; String matching

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; DNA SEQUENCES; MATHEMATICAL MODELS; OPTIMAL SYSTEMS; PROBABILITY; SET THEORY;

LOWER MUTUAL INFORMATION; SHORTEST COMMON SUPERSTRING; STRING MATCHING;

DATA COMPRESSION;

EID: 0033184599     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.782108     Document Type: Article

References (26)

1. K. S. Alexander, "Shortest common superstrings of random strings," J. Appl. Probab., to be published.
2. C. Berge, Graphs. Amsterdam, The Netherlands: Elsevier, 1985.
3. T. Berger, Rate Distortion Theory: A Mathematical Basis for Data Compression. Englewood Cliffs, NJ: Prentice-Hall, 1971.
4. A. Blum, T. Jiang, M. Li, J. Tromp, and M. Yannakakis, "Linear approximation of shortest superstrings," J. Assoc. Comput. Mach., vol. 41, no. 4, pp. 630-647, July 1994.
5. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991.
6. I. Csiszâr and J. Körner, Information Theory: Coding Theorems for Discrete Memoryless Systems. New York: Academic, 1981.
7. A. Frieze and W. Szpankowski, "A greedy algorithm for the shortest common superstring is asymptotically optimal," Algorithmica, vol. 21, pp. 21-36, 1998.
8. J. K. Gaulant, "String compression algorithms," Ph.D. dissertation, Dept. Elec. Eng. Comput. Sci., Princeton Univ., Princeton, NJ, 1982.
9. M. R. Garey and D. S. Johnson, Computers and Intractability. New York: Freeman, 1979.
10. R. M. Gray, Entropy and Information Theory. New York: Springer-Verlag, 1990.
11. W. Hoeffding, "Asymptotically optimal tests for multinomial distributions," AMS, vol. 36, pp. 369-400, 1965.
12. A. Lesk, Computational Molecular Biology, Sources and Methods for Sequence Analysis. Oxford, U.K.: Oxford Univ. Press, 1988.
13. H. Peltola, H. Söderlund, J. Tarhio, and E. Ukkonen, "Algorithms for some string matching problems arising in molecular genetics," in Information Processing 83 (Proc. IFIP Congr., 1983). Amsterdam, The Netherlands: Elsevier, 1983, pp. 53-64.
14. M. S. Pinsker, Information and Information Stability of Random Variables and Processes. San Francisco, CA: Holden-Day, 1964.
15. I. N. Sanov, "On the probability of large deviations of random variables" (in Russian), Math. Sbornik, vol. 42, pp. 11-44, 1957.
16. J. A. Storer and T. G. Szymanski, "Data compression via textual substitution," J. Assoc. Comput. Mach., vol. 29, pp. 928-951, 1982.
17. J. Tarhio and E. Ukkonen, "A greedy approximation algorithm for constructing shortest common superstrings," Theoret. Comput. Sci., vol. 57, pp. 131-145, 1988.
18. J. S. Turner, "Approximation algorithms for the shortest common superstring problem," Inform. Comput., vol. 83, no. 1, pp. 1-20, 1989.
19. A. D. Wyner and J. Ziv, "Some asymptotic properties of the entropy of a stationary ergodic data source with applications to data compression," IEEE Trans. Inform. Theory, vol. 35, pp. 1250-1258, 1989.
20. "Fixed database version of the Lempel-Ziv data compression algorithm," IEEE Trans. Inform. Theory, vol. 37, pp. 878-880, 1991.
21. E.-h. Yang and J. C. Kieffer, "On the performance of data compression algorithms based upon string matching," IEEE Trans. Inform. Theory, vol. 44, pp. 47-65, Jan. 1998.
22. "On the redundancy of the fixed database Lempel-Ziv algorithm for phi-mixing sources," IEEE Trans. Inform. Theory, vol. 43, pp. 1101-1111, July 1997.
23. E.-h. Yang and Z. Zhang, "An on-line universal lossy data compression algorithm by continuous codebook refinement-Part III: Redundancy analysis," IEEE Trans. Inform. Theory, vol. 44, pp. 1782-1801, Sept. 1998.
24. Z. Zhang, E.-h. Yang, and V. K. Wei, "The redundancy of source coding with a fidelity criterion-Part I: Known statistics," IEEE Trans. Inform. Theory, vol. 43, pp. 71-91, Jan. 1997.
25. J. Ziv and A. Lempel, "A universal algorithm for sequential data compression," IEEE Trans. Inform. Theory, vol. IT23, pp. 337-343, 1977.
26. "Compression of individual sequences via variable rate coding," IEEE Trans. Inform. Theory, vol. IT24, pp. 530-536, 1978.