Bounding the inefficiency of length-restricted prefix codes

Algorithmica (New York)

Volumn 31, Issue 4, 2001, Pages 513-529

  Milidiu R L ^a   Laber, E S ^a  

^a PONTIFICAL CATHOLIC UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Approximative algorithm; Compression; Huffman trees; Prefix codes; Redundancy

Indexed keywords

ALGORITHMS; DATABASE SYSTEMS; PROBABILITY; REDUNDANCY; TREES (MATHEMATICS);

PREFIX CODES;

CODES (SYMBOLS);

EID: 0242301669     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00453-001-0060-4     Document Type: Article

References (28)

1. D. A. Huffman, A method for the construction of minimum-redundancy codes, Proceedings of the Institute of Radio Engineers, vol. 40, no. 9, pp. 1098-1101, Sept. 1952.
2. J. van Leeuwen, On the construction of Huffman trees, in Third International Colloquium on Automata, Languages and Programming (S. Michaelson and R. Milner, eds.) (University of Edinburgh, 20-23 July 1976), pp. 382-410, Edinburgh University Press, Edinburgh, 1976.
3. A. Moffat and J. Katajainen, In-place calculation of minimum-redundancy codes, in Algorithms and Data Structures, 4th International Workshop (S. G. Akl, F. K. H. A. Dehne, J.-R. Sack, and N. Santoro, eds.), (Kingston, Ontario, 16-18 Aug. 1995), pp. 393-402, vol. 955 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, 1995.
4. E. N. Gilbert, Codes based on innacurate source probabilities, IEEE Transactions on Information Theory, vol. 17, pp. 304-314, 1971.
5. J. Zobel and A. Moffat, Adding compression to a full-text retrieval system, Software-Practice and Experience, vol. 25, pp. 891-903, Aug. 1995.
6. T. C. Hu and K. C. Tan, Path length of binary search trees, SIAM Journal on Applied Mathematics, vol. 22, pp. 225-234, 1972.
7. D. C. van Voorhis, Constructing codes with bounded codeword lengths, IEEE Transactions on Information Theory, vol. 20, pp. 288-290, 1974.
8. M. R. Garey, Optimal binary search trees with restricted maximal depth, SIAM Journal on Computing, vol. 3, pp. 101-110, June 1974.
9. L. L. Larmore and D. S. Hirschberg, A fast algorithm for optimal length-limited Huffman codes. Journal of the ACM, vol. 37, pp. 464-473, July 1990.
10. A. S. Fraenkel and S. T. Klein, Bounding the depth of search trees, The Computer Journal, vol. 36, no. 7, pp. 668-678, 1993.
11. A. Aggarwal, B. Schieber, and T. Tokuyama, Finding a minimum-weight k-link path in graphs with the concave monge property and applications, Discrete & Computational Geometry, vol. 12, pp. 263-280, 1994.
12. B. Schieber, Computing a minimum-weight k-link path in graphs with the concave Monge property, in Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms (San Francisco, California, 22-24 Jan. 1995), pp. 405-411.
13. R. L. Milidiú and E. S. Laber, The warm-up algorithm: a Lagrangean construction of length restricted Huffman codes, SIAM Journal on Computing, vol. 30, no. 5, pp. 1405-1426, 2000.
14. E. S. Laber, Um algoritmo eficiente para construção de códigos de prefixo com restrição de comprimento. Master's thesis, PUC-RJ, Rio de Janeiro, 1997.
15. R. L. Milidiu, A. A. Pessoa, and E. S. Laber, Efficient implementation of the WARM-UP algorithm for the construction of length-restricted prefix codes, in Proceedings of the ALENEX (Baltimore, Maryland), vol. 1619 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, January 1999.
16. R. M. Capocelli and A. De Santis, On the redundancy of optimal codes with limited word length, IEEE Transactions on Information Theory, vol. 38, pp. 439-445, 1992.
17. A. Turpin and A. Moffat, Practical length-limited coding for large alphabets, The Computer Journal, vol. 38, no. 5, pp. 339-347, 1995.
18. A. Moffat and A. Turpin, Efficient construction of minimum-redundancy codes for large alphabets, IEEE Transactions on Information Theory, vol. 44, pp. 1650-1657, July 1998.
19. R. L. Milidiú, A. A. Pessoa, and E. S. Laber, In-place length-restricted prefix coding, in Proceedings of SPIRE '98 (B. A. R. Neto, ed.), (Santa Cruz de La Sierra, Bolivia), pp. 50-59, IEEE Computer Society, Rockville, Maryland, September 1998.
20. S. Even, Graph Algorithms, Computer Science Press, Rockville, Maryland, 1979.
21. B. McMillan, Two inequalities implied by unique decipherability, IEEE Transaction on Information Theory, vol. 22, pp. 155-156, 1956.
22. R. Guttler, K. Mehlhorn, and W. Schneider, Binary search trees: average and worst case behaviour, Elektronik Informationsverarbeitung und Kybernetik, vol. 1, no. 3, pp. 41-61, 1980.
23. G. O. Katona and T. Nemetz, Huffman codes and self information, IEEE Transaction on Information Theory, vol. 22, pp. 337-340, 1976.
24. D. Knuth, The Art of Computer Programming, Fundamental Algorithms, vol. 1, Addison-Wesley, Reading, Massachusetts, 1968.
25. R. Gallager, Variations on a theme of Huffman, IEEE Transaction on Information Theory, vol. 24, pp. 668-674, Nov. 1978.
26. J. Katajainen, A. Moffat, and A. Turpin, A fast and space-economical algorithm for length-limited coding, in ISAAC: 6th International Symposium on Algorithms and Computation, vol. 1004, lens, 1995.
27. D. E. Knuth, Dynamic Huffman coding. Journal of Algorithms, vol. 6, pp. 163-180, June 1985.
28. J. S. Vitter, Design and analysis of dynamic Huffman codes, Journal of the ACM, vol. 34, pp. 825-845, Oct. 1987.