String Matching with Preprocessing of Text and Pattern

We consider the well known string matching problem where a text and pattern are given and the problem is to determine if the pattern appears as a substring in the text. The setting we investigate is where the pattern and the text are preprocessed separately at two different sites. At some point in time the two sites wish to determine if the pattern appears in the text (this is the on-line stage). We provide preprocessing and on-line algorithms such that the preprocessing algorithm runs in linear time and requires linear storage and the on-line complexity is logarithmic in the text. We also give an application of the algorithm to parallel data compression, and show how to implement the Lempel Ziv algorithm in logarithmic time with linear number of processors.

[1]  James A. Storer,et al.  Data Compression: Methods and Theory , 1987 .

[2]  Richard M. Karp,et al.  Efficient Randomized Pattern-Matching Algorithms , 1987, IBM J. Res. Dev..

[3]  Andrew Chi-Chih Yao,et al.  Some complexity questions related to distributive computing(Preliminary Report) , 1979, STOC.

[4]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[5]  Abraham Lempel,et al.  On the Complexity of Finite Sequences , 1976, IEEE Trans. Inf. Theory.

[6]  Michael Rodeh,et al.  Linear Algorithm for Data Compression via String Matching , 1981, JACM.

[7]  J. Van Leeuwen,et al.  Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[8]  Nimrod Megiddo,et al.  Applying parallel computation algorithms in the design of serial algorithms , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[9]  Abraham Lempel,et al.  Compression of individual sequences via variable-rate coding , 1978, IEEE Trans. Inf. Theory.

[10]  Abraham Lempel,et al.  A universal algorithm for sequential data compression , 1977, IEEE Trans. Inf. Theory.

[11]  C. Jordan.  Sur les assemblages de lignes. , 1869 .

[12]  Edward M. McCreight,et al.  A Space-Economical Suffix Tree Construction Algorithm , 1976, JACM.

[13]  Alfred V. Aho,et al.  Algorithms for Finding Patterns in Strings , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[14]  Donald E. Knuth,et al.  Fast Pattern Matching in Strings , 1977, SIAM J. Comput..

[15]  Peter Weiner,et al.  Linear Pattern Matching Algorithms , 1973, SWAT.

[16]  Z. Galil,et al.  Combinatorial Algorithms on Words , 1985 .

[17]  J. Seiferas,et al.  Efficient and Elegant Subword-Tree Construction , 1985 .