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Linear Algorithm for Data Compression via String Matching

Michael Rodeh, Vaughan R. Pratt, Shimon Even
1981 Journal of the ACM  
A linear implementation of the optimal universal data compression methods of Lempel and Ziv is described. The main tool is McCreight's algorithm for constructing suffix trees.  ...  Ziv and Lempel' s Universal Algorithm for Data Compression Zif and Lempel's universal algorithm for sequential data compression [11] is based on their definition of the complexity of finite strings.  ...  On the basis of their notion of randomness of f'mite strings, Ziv and Lempel [11] develop a universal algorithm for sequential data compression.  ... 
doi:10.1145/322234.322237 fatcat:62gmw3fchffathcd4w2shmjgxa

Indexes and Computation over Compressed Structured Data (Dagstuhl Seminar 13232)

Sebastian Maneth, Gonzalo Navarro, Marc Herbstritt
2013 Dagstuhl Reports  
As a part of the algorithm, we describe new methods for computing matching statistics which may be of independent interest. 1 3 2 3 2 34 13232 -Indexes and Computation over Compressed Structured Data License  ...  In this talk we review the main practical results on the use of list update algorithms for data compression.  ...  Specifically, for any i and j, we wish create a data structure that reports the positions of the largest k elements in A[i..j] in decreasing order, without accessing A at query time.  ... 
doi:10.4230/dagrep.3.6.22 dblp:journals/dagstuhl-reports/ManethN13 fatcat:b35at6erjbe63hvelnqnrt4jle

Universal lossless compression via multilevel pattern matching

J.C. Kieffer, En-Hui Yang, G.J. Nelson, P. Cosman
2000 IEEE Transactions on Information Theory  
A universal lossless data compression code called the multilevel pattern matching code (MPM code) is introduced.  ...  From the concatenated encoded token strings, the decoder can reconstruct the data string via several rounds of parallel substitutions.  ...  Neuhoff for bringing the -gram text compression algorithm to their attention.  ... 
doi:10.1109/18.850665 fatcat:ojppn7pmjffalgevlwxzt3vu3u

Compressed Parameterized Pattern Matching

R. Beal, D. A. Adjeroh
2013 2013 Data Compression Conference  
Pattern matching between traditional strings is well defined for both uncompressed and compressed sequences.  ...  Prior to this work, parameterized pattern matching (p-matching) was defined predominately by the matching between uncompressed parameterized strings (p-strings) from the constant alphabet Σ and the parameter  ...  Unlike in [6, 5] where p-matching via compressed strings is studied for the run-length encodings of T and P , our work differs in that (1) p-matching is performed on an uncompressed P and T c , a compressed  ... 
doi:10.1109/dcc.2013.54 dblp:conf/dcc/BealA13 fatcat:qojdw2in2jaurocwgisow4zxve

Page 67 of Journal of Research and Practice in Information Technology Vol. 19, Issue 2 [page]

1987 Journal of Research and Practice in Information Technology  
., PRATT, V.R. and EVEN, S. (1981): Linear algorithms for data compression via string matching, Journal of the ACM, 28, 1, pp. 16-24.  ...  A Linear Algorithm for Data Compression puter (actually a COMPAQ using an 8 MHz Intel 80286 CPU chip) in Turbo Pascal.  ... 

Compressed parameterized pattern matching

Richard Beal, Donald Adjeroh
2016 Theoretical Computer Science  
Pattern matching between traditional strings is well defined for both uncompressed and compressed sequences.  ...  Prior to this work, parameterized pattern matching (p-matching) was defined predominately by the matching between uncompressed parameterized strings (p-strings) from the constant alphabet Σ and the parameter  ...  Unlike in [6, 5] where p-matching via compressed strings is studied for the run-length encodings of T and P , our work differs in that (1) p-matching is performed on an uncompressed P and T c , a compressed  ... 
doi:10.1016/j.tcs.2015.09.015 fatcat:3drdwykatbc4dfuks3kri5bpjm

Page 9564 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
Summary: “A writer stores some data in memory accessible via address lines.  ...  The authors present a linear time and linear space algorithm for finding the length of every repeated suffix of every nonempty prefix of string p.  ... 

The effect of flexible parsing for dynamic dictionary-based data compression

Y. Matias, N. Rajpoot, S.C. Sahinalp
1999 Proceedings DCC'99 Data Compression Conference (Cat. No. PR00096)  
We also introduce a new fingerprint based data structure which enables efficient, linear time implementation.  ...  The new data structure based on fingerprints [KR87] , is randomized, and guarantees an expected linear running time for the algorithm.  ...  However it was noted that: "An optimal parsing scheme would also have to consider the possibility of matching a short first string and then a short second string in order to match a very long third string  ... 
doi:10.1109/dcc.1999.755673 dblp:conf/dcc/MatiasRS99 fatcat:pfuutdfnbvh2bonp3fb6yawkfu

The Effect of Flexible Parsing for Dynamic Dictionary-Based Data Compression

Yossi Matias, Nasir Rajpoot, Cenk Sahinalp
2001 ACM Journal of Experimental Algorithmics  
We also introduce a new fingerprint based data structure which enables efficient, linear time implementation.  ...  The new data structure based on fingerprints [KR87] , is randomized, and guarantees an expected linear running time for the algorithm.  ...  However it was noted that: "An optimal parsing scheme would also have to consider the possibility of matching a short first string and then a short second string in order to match a very long third string  ... 
doi:10.1145/945394.945404 fatcat:zytnoyda4jgibnpxnwevq3at3u

A prefix array for parameterized strings

Richard Beal, Donald A. Adjeroh, W.F. Smyth
2017 Journal of Discrete Algorithms  
Then, we show how to construct the compact prefix array for hp-strings. Finally, we discuss applications for our data structures.  ...  In this work, we identify the connection between the p-match and music, one of several applications to motivate our study of holes in p-strings, and prefix array-based data structures for p-strings.  ...  In this work, we extend the P A/cP A framework for p-strings and provide a linear time construction via a novel use of the parameterized longest previous factor (pLP F ) data structure.  ... 
doi:10.1016/j.jda.2016.11.002 fatcat:qptzx7ukmvhsdksohqk57tdqd4

Suffix sorting via matching statistics [article]

Zsuzsanna Lipták and Francesco Masillo and Simon J. Puglisi
2022 arXiv   pre-print
We introduce a new algorithm for constructing the generalized suffix array of a collection of highly similar strings.  ...  As a first step, we construct a compressed representation of the matching statistics of the collection with respect to a reference string.  ...  Since then, several authors have described similar algorithms for computing matching statistics, all focussed on reducing space requirements via the use of compressed indexes instead of the suffix tree  ... 
arXiv:2207.00972v1 fatcat:phgfh6jlgncydmxjqob6bpjfse

Optimal parallel dictionary matching and compression (extended abstract)

Martin Farach, S. Muthukrishnan
1995 Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures - SPAA '95  
Parallel Dictionary Matching and Compression (Extended Abstract)  ...  For each dominating match i, we find the next dominating match AJ[i] via all nearest ones (See Lemma 2.4). For each dominating i, we do the following.  ...  Within two years of the dis- covery of the classical linear time string matching algo- rithm due to Knuth, Morris and Pratt [19], Aho and Corasick [3] designed a linear time (hence, optimal  ... 
doi:10.1145/215399.215451 dblp:conf/spaa/FarachM95 fatcat:5xlpmwfmsbay7et6iqdshogly4

Sublinear Matching With Finite Automata Using Reverse Suffix Scanning [article]

Steven M. Kearns
2015 arXiv   pre-print
We give algorithms for constructing an OFA that accepts the same language as a DFA while possibly skipping input, and for matching with an OFA.  ...  Compared to previous algorithms that attempt to skip some of the input, the new matching algorithm can skip more often and can skip farther.  ...  Since matching sets of strings is a subset of the regular expression matching problem, the OFA algorithm can theoretically replace all string matching algorithms that match sets of strings.  ... 
arXiv:1308.3822v3 fatcat:5z7hkia25rclveqapnw3etiea4

String Indexing with Compressed Patterns [article]

Philip Bille and Inge Li Gørtz and Teresa Anna Steiner
2021 arXiv   pre-print
Our main result is a novel linear space data structure that achieves near-optimal query time for patterns compressed with the classic Lempel-Ziv compression scheme.  ...  Along the way we develop several data structural techniques of independent interest, including a novel data structure that compactly encodes all LZ77 compressed suffixes of a string in linear space and  ...  In Section 2 we recall basic string data structures and LZ77 compression.  ... 
arXiv:1909.11930v4 fatcat:2zi5r4eukrea3dmkbnzxjjq4pm

String Indexing with Compressed Patterns

Philip Bille, Inge Li Gørtz, Teresa Anna Steiner, Markus Bläser, Christophe Paul
2020 Symposium on Theoretical Aspects of Computer Science  
Our main result is a novel linear space data structure that achieves near-optimal query time for patterns compressed with the classic Lempel-Ziv 1977 (LZ77) compression scheme.  ...  Along the way we develop several data structural techniques of independent interest, including a novel data structure that compactly encodes all LZ77 compressed suffixes of a string in linear space and  ...  As before, we additionally store the suffix array, the range within the suffix array for each node, and a linear-sized lcp data structure for S. Algorithm The algorithm proceeds as follows.  ... 
doi:10.4230/lipics.stacs.2020.10 dblp:conf/stacs/BilleGS20 fatcat:73nxlfr54rbtfiik6grnjkgp6i
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