Abstract
We survey the complexity issues related to several algorithmic problems for compressed one- and two-dimensional texts without explicit decompression: pattern-matching, equality-testing, computation of regularities, subsegment extraction, language membership, and solvability of word equations. Our basic problem is one- and two-dimensional pattern-matching together with its variations. For some types of compression the pattern-matching problems are unfeasible (NP-hard), for other types they are solvable in polynomial time and we discuss how to reduce the degree of corresponding polynomials.
Supported by the grant KBN 8T11C03915.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The design and analysis of computer algorithms, Addison-Wesley, Reading, Mass., 1974.
A. Amir, G. Benson and M. Farach, Let sleping files lie: pattern-matching in Z-compressed files. Journal of Computer and System Sciences, 1996, Vol. 52, No. 2, pp. 299–307.
A. Amir, G. Benson, Efficient two dimensional compressed matching, Proceedings of the 2nd IEEE Data Compression Conference, pp. 279–288 (1992).
A. Amir, G. Benson and M. Farach, Optimal two-dimensional compressed matching, Journal of Algorithms, 24(2):354–379, August 1997.
Angluin D., Finding patterns common to a set of strings, J.C.S.S., 21(1), 46–62, 1980.
S. De Agostino, P-complete problems in data compression, Theoretical Computer Science 127, 181–186, 1994.
S. De Agostino, Pattern-matching in text compressed with the ID heuristic, in J. Atorer, and M. Cohn (Editors), Data Compression Conference 1998, IEEE Computer Society, pp. 113–118.
M. F. Barnsley, L. P. Hurd, Fractal image compression, A. K. Peters Ltd. 1993.
P. Berman, M. Karpinski, L. L. Larmore, W. Plandowski, and W. W. Rytter, On the Complexity of Pattern Matching for Highly Compressed Two-Dimensional Texts, Proceedings of the 8th Annual Symposium on Combinatorial Pattern Matching LNCS 1264, Edited by A. Apostolico and J. Hein, (1997), pp. 40–51.
M. Crochemore, F. Mignosi, A. Restivo, S. Salemi, Text compression using antidictionaries, ICALP 1999.
M. Crochemore and W. Rytter, Text Algorithms, Oxford University Press, New York (1994).
M. Crochemore, W. Rytter, Efficient parallel algorithms to test square-freeness and factorize strings, Information Processing Letters, 38 (1991) 57–60.
K. Culik and J. Karhumäki, Finite automata computing real functions, SIAM J. Comp (1994).
K. Culik and J. Kari, Image compression using weighted finite automata, Computer and Graphics 17, 305–313 (1993).
K. Culik and J. Kari, Fractal image compression: theory and applications, (Ed. Y. Fisher), Springer Verlag 243–258 (1995).
D. Derencourt, J. Karhumäki, M. Letteux and A. Terlutte, On continuous functions computed by real functions, RAIRO Theor. Inform. Appl. 28, 387–404 (1994).
S. Eilenberg, Automata, Languages and Machines, Vol.A, Academic Press, New York (1974).
M. Farach and M. Thorup, String matching in Lempel-Ziv compressed strings, Proceedings of the 27th Annual Symposium on the Theory of Computing (1995), pp. 703–712.
M. Farach, S. Muthukrishnan, Optimal Parallel Dictionary Matching and Compression SPAA 1995.
J. Karhumaki, W. Plandowski, W. Rytter, Pattern matching for images generated by finite automata, FCT’97, in LNCS Springer Verlag 1997.
M. Gu, M. Farach, R. Beigel, An Efficient Algorithm for Dynamic Text Indexing (SODA’ 94).
M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, New York (1979).
L. Gąsieniec, M. Karpinski, W. Plandowski and W. Rytter, Efficient Algorithms for Lempel-Ziv Encoding, Proceedings of the 5th Scandinavian Workshop on Algorithm Theory. Springer-Verlag (1996).
L. Gasieniec, M. Karpinksi, W. Plandowski, W. Rytter, Randomized algorithms for compressed texts: the finger-print approach, Combinatorial Pattern Matching 1996, Lecture Notes in Comp. Science, Springer Verlag 1996.
L. Gasieniec, W. Rytter, Almost optimal fully compressed LZW-matching,in Data Compression Conference, IEEE Computer Society 1999.
L. Gasieniec, A. Gibbons, W. Rytter, The parallel complexity of pattern-searching in highly compressed texts, in MFCS 1999.
A. Gibbons, W. Rytter, Efficient parallel algorithms, Cambridge University Press 1988.
O. H. Ibarra and S. Moran, Probabilistic algorithms for deciding equivalence of straight-line programs, JACM 30 (1983), pp. 217–228.
J. Karhumaki, W. Plandowski, W. Rytter, The compression of subsegments of compressed images, in Combinatorial Pattern Matching 1999.
Karhumäki J., Mignosi F., Plandowski W., The expressibility of languages and relations by word equations, in ICALP’97, LNCS 1256, 98–109, 1997.
R. M. Karp, Reducibility among combinatorial problems, in “Complexity of Computer Computations”, Plemum Press, New York, 1972 (Editors R. E. Miller and J. W. Thatcher).
T. Kida, M. Takeda, A. Shinohara, S. Arikawa, Sfift-and approach to pattern matching in LZW compressed text, Combinatorial Pattern-Matching 1999, LNCS 1645, pp.1–13.
T. Kida, M. Takeda, A. Shinohara, M. Miyazaki, S. Arikawa, Multiple patter-matching in LZW compressed text, in J. Atorer, and M. Cohn (Editors), Data Compression Conference 1998, IEEE Computer Society, pp. 103–112.
M. Karpinski, W. Rytter and A. Shinohara, Pattern-matching for strings with short description, Nordic Journal of Computing, 4(2):172–186, 1997.
J. Kari, P. Franti, Arithmetic coding of weighted nite automata,,RAIRO Theor. Inform. Appl. 28 343–360 (1994).
R. M. Karp and M. Rabin, Efficient randomized pattern matching algorithms,IBM Journal of Research and Dev. 31, pp. 249–260 (1987).
D. Knuth, The Art of Computing, Vol. II: Seminumerical Algorithms. Second edition. Addison-Wesley (1981).
A. Lempel and J. Ziv, On the complexity of finite sequences, IEEE Trans. on Inf. Theory 22 (1976) pp. 75–81.
A. Lempel and J. Ziv, Compression of two-dimensional images sequences,Combinatorial algorithms on words (Ed. A. Apostolico, Z. Galil), Springer-Verlag (1985) pp.141–156.
M. Lothaire, Combinatorics on Words. Addison-Wesley (1993).
Makanin, G. S., The problem of solvability of equations in a free semigroup, Mat. Sb., Vol. 103,(145), 147–233, 1977. English transl. in Math. U.S.S.R. Sb. Vol 32,1977.
U. Manber, A text compression scheme that allows fast searching directly in the compressed file, ACM Transactions on Information Systems, 15(2), pp.124–136, 1997.
M. Miyazaki, A. Shinohara, M. Takeda, An improved pattern-matching algorithm for strings in terms of straight-line programs, Combinatorial Pattern-Matching 1997, LNCS 1264, pp. 1–11.
R. Motwani, P. Raghavan, Randomized Algorithms, Cambridge University Press (1995).
E. de Moura, G, Navarro, N. Ziviani, R. Baeza-Yates, Direct pattern-matching on compressed text, in SPIRE, pp.90–95, IEEE CS Press, 1998.
E. de Moura, G, Navarro, N. Ziviani, R. Baeza-Yates, Fast sequential searching on compressed texts allowing errors, 21st Annual Int. ACM SIGIR Conference on Research and Development in Information retrieval, pp. 298–306, York Press 1998.
G. Navarro, M. Raffinot, A general practical approach to pattern-matching over Zil-Lempel compressed text, Combinatorial Pattern-Matching 1999, LNCS 1645, pp. 14–36.
Ch. H. Papadimitriou, Computational Complexity, Addison Wesley (1994).
H. O. Peitgen, P. H. Richter, The beauty of plants, Springer-Verlag 1986.
W. Plandowski, Testing equivalence of morphisms on context-free languages, Proceedings of the 2nd Annual European Symposium on Algorithms (ESA’94), LNCS 855, Springer-Verlag (1994), pp. 460–470.
W. Plandowski, Solvability of word equations with constants is in NEXPTIME, STOC 1999.
W. Plandowski, Solvability of word equations with constants is in P-SPACE, FOCS 1999.
W. Plandowski, W. Rytter, Complexity of compressed recognition of formal languages, in “Jewels forever”, Springer Verlag 1999 (Ed. J. Karhumaki).
W. Plandowski, W. Rytter, Applying Lempel-Ziv encodings to the solution of word equations, ICALP 1998.
J. Schwartz, Fast probabilistic algorithms for verification of polynomial identities, J. ACM 27 (1980) pp. 701–717.
J. Shallit, D. Swart, An efficient algorithm for computing the i-th letter of ∅n(a), SODA 1999.
Y. Shibata, M. Takeda, A. Shinohara, S. Arikawa,Pattern-matching in text compressed by using antidictionaries,Combinatorial Pattern-Matching 1999,LNCS 1645,pp.37.
J. Storer, Data compression: methods and theory, Computer Science Press (1988).
R. E. Zippel, Probabilistic algorithms for sparse polynomials, Proceedings of the International Symposium on Symbolic and Algebraic Manipulation (EUROSAM’ 79) LNCS 72, Springer-Verlag (1979), pp. 216–226.
J. Ziv and A. Lempel, A Universal algorithm for sequential data compression, IEEE Transactions on Information Theory IT-23 (1977), pp. 337–343.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rytter, W. (1999). Algorithms on Compressed Strings and Arrays. In: Pavelka, J., Tel, G., Bartošek, M. (eds) SOFSEM’99: Theory and Practice of Informatics. SOFSEM 1999. Lecture Notes in Computer Science, vol 1725. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47849-3_3
Download citation
DOI: https://doi.org/10.1007/3-540-47849-3_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66694-3
Online ISBN: 978-3-540-47849-2
eBook Packages: Springer Book Archive