J. A. Storer and T. G. Szymanski. Data Compression via Textual Substitution. Journal of the ACM, 29:928--951, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....strings S = s 1 #: #s n ) produces a mapping = A (S) We define A (S) S) and OE A (S) OE (S) SCS was shown to be NP complete by Maier and Storer in [8] Another, and more elegant proof appears in [3] and [4] One obvious application for the problem is data compression. Storer and Szymanski [15] for example, consider a fairly general model of data compression which includes SCS as an important special case. See also [9] Another application is to DNA sequencing. SCS is one of the simplest models for the problem of recovering DNA sequencing information from experimental data [5, 12, 14] ....

Storer, James A. and Thomas G. Szymanski. "Data Compression via Textual Substitution," Journal of the ACM, vol. 29, 10/82, 928--951.

....to be NP hard ( 2, 9] The length constraint would be useful only if the target superstring is expected to be the shortest one. In biological applications, this is usually not the case. Interest in designing efficient algorithms for SAP has mainly been prompted by problems in data compression ([2, 11]) and computational biology ( 5, 4, 13] A combinatorial solution to the DNA sequencing problem has been a topic of research for over a decade. The early approaches ( 3, 10] that use classical biological techniques are comparatively slow making these methods impractical for large problem sizes. ....

J. Storer, T. Szymanski "Data Compression via textual substitution," J. ACM, 29, pp. 928-951, 1982.

....are only an approximation of the nal compression levels obtained with a code of this nature as necessary information that describes the Hu man codes employed (a prelude) is not included in these estimates. O ine compression through the use of a phrase book is not a new idea [Rubin, 1976, Storer Szymanski, 1982, Nevill Manning Witten, 1994] but with the increased availability of cheap, powerful computers, computationally intensive techniques are now viable during encoding in order to improve compression levels through the construction of good phrase books. The task of identifying the best possible ....

....availability of cheap, powerful computers, computationally intensive techniques are now viable during encoding in order to improve compression levels through the construction of good phrase books. The task of identifying the best possible phrase book on any input has been shown to be NP complete [Storer Szymanski, 1982], but using heuristics and a lot of machine power, compression levels superior to alternate techniques have been achieved on some data sets. Nevill Manning Witten introduced an approach that induces a context free grammar from the text, using their grammar rules to describe the phrase book for ....

Storer, J. A. & Szymanski, T. G. (1982). Data compression via textual substitution. Journal of the ACM, 29:928-951.

....using the terms coined in [2] the citation, namely the longest prefix phrase that has already accommodated in the dictionary, and the innovation, the symbol immediately following the citation. The citation and the innovation can be then encoded individually or jointly. It is widely observed ([7, 11]) that such encoding cost might be excessive since the coding for innovation contributes around log 2 # bits, where # is the size of the input alphabet set. One of the strategies to overcome such wastage is to defer the encoding of innovation as the first symbol of the next parsing, thus it will ....

J.A. Storer and T.G. Szymanski. Data compression via textual substitution. Journal of ACM, 29(4):928--951, 1982.

....using the terms coined in [2] the citation, namely the longest pre x phrase that has already accommodated in the dictionary, and the innovation, the symbol immediately following the citation. The citation and the innovation can be then encoded individually or jointly. It is widely observed ([7, 11]) that such encoding cost might be excessive since the coding for innovation contributes around log 2 bits, where is the size of the input alphabet set. One of the strategies to overcome such wastage is to defer the encoding of innovation as the rst symbol of the next parsing, thus it will ....

J.A. Storer and T.G. Szymanski. Data compression via textual substitution. Journal of ACM, 29(4):928-951, 1982.

....Chapter 4. In 1984, Welch increased the eciency of LZ78 with a new procedure, now known as LZW [37] In practice, LZW is much preferred over LZ78, but for our purposes the di erence is small. Also in the 1970 s, Storer and Szymanski were exploring a wide range of macrobased compression schemes [33, 35, 34]. They de ned a collection of attributes that such a compressor might have, such as recursive , restricted , overlapping , etc. Each combination of these adjectives described a di erent scheme, many of which they considered in detail. Apparently, none of these was precisely the context free ....

....in Section 3.4. 3.1 NP Hardness Theorem 5 There is no polynomial time algorithm for the smallest grammar problem with approximation ratio less than 8569=8568 unless P = NP. Proof. We use a reduction from a restricted form of vertex cover based closely on arguments by Storer and Szymanski [35, 34]. Let H = V; E) be a graph with maximum degree three and jEj jV j. We can map the graph H to a string over an alphabet that includes a distinct terminal (denoted v i ) corresponding to each vertex v i 2 V as follows: #v i j v i # j) #v i # j) v i ;v j )2E (#v i #v j # j) ....

James A. Storer and Thomas G. Szymanski. Data compression via textual substitution. Journal of the ACM, 29(4):928-951, October 1982.

....a statistical method, where strings with a high frequency of occurrence are assigned shorter codes than strings with a low frequency. The svc compression scheme is a combination of both. Terms are compressed by a combination of dynamic Hu#man encoding [11] and a Lempel Ziv variant based on LZSS [15]. That is, each first occurrence of a substring is compressed by this LZSS variant, preceded by an escape sequence, and assigned a code. Each other occurrence of this substring is then represented by its code, which is subject to change according to the dynamic Hu#man algorithm which assures that ....

....by an escape sequence, and assigned a code. Each other occurrence of this substring is then represented by its code, which is subject to change according to the dynamic Hu#man algorithm which assures that frequent codes are shorter than less frequent ones. The Lempel Ziv variant is based on LZSS [15] with the one deviation that the search bu#er is stored in the same circular queue as the look ahead bu#er, instead of storing it in a binary search tree. The tokens consist of one flag bit followed by 8 length bits and 15 o#set bits (flag = 1) or the 7 least significant bits of an ASCI character ....

Storer, J., and Szymanski, T. Data compression via textual substitution. Journal of the

....in the dictionary is recorded to compress the phrase. Some compression utilities available on personal computers and workstations (such as PKZIP [6] and compress ) implement variations of the LZW method. The Lempel Ziv Storer Szymanski (LZSS) algorithm keeps track of the last n bytes of data [7]. When a phrase that has appeared before is encountered, the phrase is encoded as a pair of values corresponding to the position of the phrase in the buffer and the length of the phrase. Besides the above general data compression algorithms, there are many compression methods designed for special ....

....sequence for a pin of circuit S1 was 14,840, and it was reduced to 3 after the BW transformation. The next experiment we performed was to compare the compression ratio of the proposed method with that of six well known compression methods, Huffman [1] arithmetic coding [2] compress, gzip, LZSS [7], and LZW [5] For the experiments, we implemented Huffman, arithmetic, LZW, and LZSS methods based on the programs available in [8] and used UNIX and GNU utilities for compress and gzip , respectively. Table 5 shows compression ratios achieved for the seven different methods. The size of D i ....

J.A. Storer and T.G. Szymanski, "Data Compression via Textual Substitution," Journal of ACM, Vol. 29, No. 4, October 1982, pp. 928-951.

....of Informatics, Kyushu University, Fukuoka 8128581, Japan. E mail: fhiroshi, ayumi, takedag i.kyushuu. ac.jp z Dept. of Arti cial Intelligence, Kyushu Institute of Technology, Iizuka 820 8502, Japan. E mail: sin ai.kyutech.ac. jp often referred to as LZ77 and LZ78, and their variants (e.g. [15, 13]) are most widely used universal lossless compression algorithms, together with the arithmetic coding algorithms (see, e.g. 11] Finding the minimum representation of a given text string is regarded as a combinatorial optimization problem. One interesting topic is to analyze the time ....

J. Storer and T. Szymanski. Data compression via textual substitution. J. Assoc. Comput. Mach., 29(4):928-951, 1982.

....be decompressed and loaded into RAM. Thus, savings are achieved only on secondary storage. These techniques are not directly suitable for minimizing code size in embedded systems with limited on chip program ROMs. We have opted for a simple model known as the external pointer macro (EPM) model [2]. In this model, compressed data consists of a dictionary and a skeleton. The dictionary contains substrings that occur frequently in the original data. The skeleton contains symbols from the alphabet of the original data, interspersed with pointers to the dictionary. This model suits our approach ....

J. A. Storer and T. G. Szymanski. Data Compression via Textual Substitution. Journal of the ACM, 29(4):928--951, October 1982.

....structure are different. In comparison with Crusher, MXT offers substantially smaller compression decompression latency and notably improved compression and storage efficiency. The compressors used in the above systems and designs are in the class termed compression by textual substitution (e.g. [10]) or, alternatively, Lempel Ziv compression [11] Early work on this class of algorithms appears in [12] These operate by substituting repeated phrases by pointers to other occurrences within the block of data to be compressed, or to a dictionary of such phrases. For cases in which general data ....

....constraint is required, that of single pass encoding decoding (the latter being a requirement for low latency) Single pass encoding decoding is a property of LZ77, X Match, and other LZ like algorithms. However, it is not a necessary condition for compression via textual substitution (see [10, 15]) Let B(1) B(2) B(n) be some ordering of the data A(1) A(2) A(n) Suppose we partition this block into k sub blocks, each of length n k, and use k compressors to compress (in parallel) each such subblock, with the condition that each compressor may find matching phrases in any of ....

J. Storer and T. Szymanski, "Data Compression via Textual Substitution," J. ACM 29, No. 4, 928--951 (1982).

....use of binary trees [5] hashing [6, 7] and Patricia trees [8] The question of how to parse the original text into a sequence of substrings is a problem common to all dictionarybased compression techniques. An optimal technique for a static dictionary is mentioned in [9] Storer and Szymanski [10] give an optimal parsing algorithm for the sliding window method, and Hirschberg and Stauffer [11] present parallel algorithms for optimal parsing. Generally, for static dictionary techniques, the parsing is done by a greedy method, i.e. at any stage, the longest matching element from the ....

....and are used in commercial compression systems. We show that their encoding functions # obey the triangle inequality, which is a sufficient condition for applying the above pruning algorithm. The first example, based on Whiting et al. 16] is a variant of LZ77 known as LZSS (Storer and Szymanski [10]) using hashing on character pairs to locate (the beginning of) recurrent strings, as in [7] The output of the compression process is thus a sequence of elements, each being either a single (uncompressed) character, or an offset length pair (d, #) The elements are identified by a flag bit, so ....

Storer, J. A. and Szymanski, T. G. (1982) Data compression via textual substitution. J. ACM, 29, 928--951.

....entries replacing the oldest entries among the table. This can be done simply by left shifting symbols in the encoding buffer by C l 1. Figure 1 shows the compression procedure of the Lempel Ziv algorithm. Several modifications have been made to further improve the compression performance [2][8]. 3. A PARALLEL LZ ALGORITHM A straightforward sequential implementation of LempelZiv data compression takes O(N M ) time to process a string of M symbols. As the amount of data to be communicated has exploded in the past few years, a sequential implementation quickly becomes inadequate to ....

J. Storer and T. Szymanski, "Data Compression via Textual Substitution," Journal of ACM 29, pp. 928-951, 1982.

....is extremely simple (i.e. memory access) while compression is computation8 intensive. Hence, it is well suited for client server environments. ffl Produces fixed length codewords which are suitable for Byte oriented network protocols. ffl Can limit the extent of possible data expansion [16]. The first Lempel Ziv algorithm is based on the concept of encoding a string of source symbols whose length is less than a prescribed integer M via a fixed length codeword, C i = C l C p . The pointer(C p ) and the matching length(C l ) indicate the position and the length respectively of the ....

Storer, J. and Szymanski, T.G., "Data Compression via Textual Substitution," Journal of ACM, pp. 928-951 October, 1982.

....of the factor to encode are searched in a window. In the second one, the LZ78 algorithm [ZL78] a dictionary containing the already encoded factors is used. Different extensions were proposed to the algorithms LZ77 and LZ78. Among others, we tested the methods LZSS (extension of LZ77) SS82] and LZW [Wel84] and compress (both extensions of LZ78) On DNA sequences, the compression rates are all negative (see 1 The DNA sequences of Figure 3 include complete genomes, genes and viruses. Here are their precise description (the numbers indicate their size) Complete genomes of two ....

J. A. Storer and T. G. Szymansk. Data compression via textual substitution. Journal of the ACM, 29(4):928--951, 1982.

....Indeed, methods based on dictionary are generally not complete [Wel84] They may loose a high percentage of factors. In general, windows have a fixed width. If s is the window s width and i is the current position, the window ranges between the (i Gamma s) ith and the i ith character [SS82, FG89] The use of small windows is efficient on texts whose redundancy is local. However, in the case of DNA sequences, redundancies may occur at very long distances and factors can be very long. We therefore allow a window of the size of the input. As shown in the previous section, there are ....

J. A. Storer and T. G. Szymansk. Data compression via textual substitution. Journal of the ACM, 29(4):928--951, 1982.

....the computing complexity and memory requirement for a statistical compressor are often much higher than a substitutional compressor. Substitutional compressors achieve high compression ratio at the high speed and there is a simple mechanism to prevent data expansion rather than compression [18]. Yet, they require relatively high set up time to adapt to the data; hence, it is not particularly effective for short data. Adaptive arithmetic coding can achieve theoretically optimum compression at the expense of slow speed due to very complex computation required. It can also result in data ....

Storer, J. and Szymanski, T.G., "Data Compression via Textual Substitution," Journal of ACM, pp. 928-951 October, 1982.

....it, then the original data will be expanded rather than compressed [3] Furthermore, the use of an explicit character (i.e. last symbol) in a codeword is wasteful because a character takes a finite number of bits to represent and could often be included in the next codeword. Storer and Szymanski [16] proposed a modified scheme called LZSS where both codewords and explicit source symbols are used for representing compressed data. To further improve the compression performance, several different modifications have been made. LZB [3] achieves better compression than LZSS by statistically ....

Storer, J. and Szymanski, T.G., "Data Compression via Textual Substitution," Journal of ACM, pp. 928-951 October, 1982.

....s i as a substring, i.e. there exist u i and v i such that # can be written as u i s i v i .Theshortest superstring problem (SSP) is to find a minimum length superstring for any given set S. One obvious application for the shortest superstring problem is data compression. Storer and Szymanski [14, 15], for example, considered a fairly general model of data compression which includes the SSP as an important special case. See also Mayne and James [9] Another application is to DNA sequencing. The SSP is one of the simplest models for the problem of recovering DNA sequencing information from ....

J. Storer and T. Szymanski, Data compression via textual substitution, J. Assoc. Comput. Mach., 29 (1982), pp. 928--951.

.... entry corresponds to the rules B C grammar C a context free This sub optimal phrase identification is an unfortunate, but inevitable, consequence of the fast algorithm we use: in fact, the problem of finding a dictionary that produces the smallest phrasestructure representation is NP complete (Storer and Szymanski, 1982). The first column gives a lexical picture of how the word grammar is used. In the second column, we focus on the first rule rule A above and list those places in the grammar where it appears. The entries flanked by ellipses indicate extracts from rule S, the top level rule, and so rule A ....

Storer, J.A. and Szymanski, T.G. (1982) "Data compression via textual substitution." J Association for Computing Machinery 29(4), 928--951.

....1977) is to require that a character is always transmitted after each pointer. Better compression is achieved by transmitting a character only when necessary. This requires transmitting an extra bit at each coding step to indicate whether the next code represents a pointer or a literal character. Storer and Szymanski (1982) and Bell (1986a) give examples of this technique. A third method takes advantage of the observation that novel characters tend to occur in groups. In this method, a code is transmitted to indicate the number of non matching characters, which are then transmitted consecutively (Fiala Green, ....

Storer, J.A., & Szymanski, T.G. (1982). Data compression via textual substitution. Journal of the ACM, 29:928--951.

....image understanding ( 22] p. 289) compiler design [1] and language modeling ( 10] Theorems 4.5, 4.6) In this paper, we shall be interested in using context free grammars for lossless data compression. There has been some previous work of this nature, including the papers [3] 2] 11] 14] [24] [18] Two approaches have been used. In one of these approaches (as illustrated in [2] 11] 14] one fixes a context free grammar G, known to both encoder and decoder, such that the language generated by G contains all of the data strings that are to be compressed. To compress a particular data ....

....contains all of the data strings that are to be compressed. To compress a particular data string, one then compresses the derivation tree ( 2] p. 844) showing how the given string is derived from the start symbol of the grammar G. In the second of the two approaches (exemplified by the papers [3] [24] [18] a different context free grammar G x is assigned to each data string x, so that the language generated by G x is fxg. If the data string x is to be compressed, the encoder transmits codebits to the decoder that allow reconstruction of the grammar G x , from which the decoder infers x. This ....

J. Storer and T. Szymanski, "Data Compression via Textual Substitution," Jour. Assoc. Comput. Mach., vol. 29, pp. 928--951, 1982.

....describes some applications and experiments. Keywords: o line textual substitution, dynamic text compression, compression of biological sequences, grammatical inference, substring statistics, augmented sux tree. I. Introduction In data compression by textual substitution (see, e.g. 1] 2] [3]) substrings with multiple occurrences in a textstring are replaced by a suitable set of pointers to a unique common copy (for instance, by giving (1) a textstring position starting from which the substring can be recopied, and (2) the length of that substring) Disparate conventions, regarding ....

.... of entries, and average length) Partly in response to this fact, techniques were devised for the compact encoding of integers in an unbounded domain (see, e.g. 4] 5] 6] Unfortunately, however, the optimal implementation of the majority of macro schemes translates into NP complete problems [3], even before the problem of encoding of pointers is taken into account. One noteworthy exception to Work supported in part by NSF Grants CCR 9201078 and CCR 9700276, by NATO Grant CRG 900293, by British Engineering and Physical Sciences Research Council Grant GR L19362, by Purdue Research ....

[Article contains additional citation context not shown here]

J. A. Storer and T. G. Szymanski, \Data compression via textual substitution," Journal of the ACM, vol. 29, no. 4, pp. 928-951, Oct. 1982.

....text of size n encoded by LZ77 into a collage system with #D# = O(n log n) 7] Below we give a translation of the LZSS compression method which is a simplified variant of LZ77. The differences between LZSS and LZ77 are essentially the same as those between LZW and LZ78. LZSS compression. [18] S = X q 1 , X q 2 , X q n , and D is as follows: X 1 = a 1 ; X 2 = a 2 ; X q = a q ; X q 1 = # # [i 1 ] X #(1) X #(1) 1 X r(1) # m1 # [j 1 ] b 1 ; X q n = # # [i n ] X #(n) X #(n) 1 X r(n) # mn # [j n ] b n ; where 0 # i k , j k , m k and b k # ....

J. Storer and T. Szymanski. Data compression via textual substitution. J. Assoc. Comput. Mach., 29(4):928--951, Oct 1982.

....IFetch. The experimental results in this paper show that neglecting IFetch performance may lead to incorrect conclusions about the appropriate scheme to implement. An interesting study by Liao, et al. 14] employs an effective compression algorithm (External Pointer Model by Storer and Szymanski [22]) on assembly level code with an average of 30 code size reduction. Two implementations, software only and call dictionary are considered. Both increase the number of branches in the code and (reportedly insignificantly) the op count. Also due to high granularity, some opportunities for ....

J.A. Storer, T.G. Szymanski "Data Compression via Textual Substitution" Journal of the ACM, 29(4) pp. 928-951, October 1982.

....text of size n encoded by LZ77 into a collage system with #D# = O(n log n) 5] Below we give a translation of the LZSS compression method which is a simplified variant of LZ77. The di#erences between LZSS and LZ77 are essentially the same as those between LZW and LZ78. LZSS compression. [15] S = X q 1 , X q 2 , X q n , and D is as follows: X 1 = a 1 ; X 2 = a 2 ; X q = a q ; X q 1 = # # [i 1 ] X #(1) X #(1) 1 X r(1) # m 1 # [j 1 ] b 1 ; X q n = # # [i n ] X #(n) X #(n) 1 X r(n) # mn # [j n ] b n ; where 0 # i k , j k , ....

J. Storer and T. Szymanski. Data compression via textual substitution. J. Assoc. Comput. Mach., 29(4):928--951, Oct 1982.

....would have such serious consequences in terms of computational complexity that it would be completely impossible to form grammars of anything like this size. In fact, the problem of finding a set of phrases that produces the smallest phrase structure representation is known to be NP complete (Storer and Szymanski, 1982). Figure 4c shows expansions of the second phrase of Figure 4b, context free grammar. This section of the hierarchy corresponds to rules E context free grammar F probabilistic E G reduced E H E cfg I E recognition etc. The phrases probabilistic context free grammar, reduced context ....

Storer, J.A. and Szymanski, T.G. (1982) "Data compression via textual substitution." J Association for Computing Machinery 29(4), 928--951.

....state. 4. PARALLEL DICTIONARY COMPRESSION Dictionary compression (also referred to as Ziv Lempel compression or textual substitution) removes data redundancy by replacing repeated input substrings by references (also called indices or pointers) to earlier copies of the identical substring [RPE81, SS82, ZL77, ZL78]. A dictionary of characters, words or phrases that are expected to occur frequently is maintained and a recurring substring is encoded by the index of its corresponding dictionary entry. Compression is achieved by choosing indices so that on average they require less space than the phrase they ....

Storer, J. A. and Szymanski, T. G. Data compression via textual substitution. J. ACM 29, 4 (1982), 928--951.

....dictionary and text are then entropy coded. Thus, each token in the text may represent a long string of characters when uncompressed. Decompression consists of reading a token and recursively looking it up in the dictionary. The general approach is not new. Finding the best dictionary is NP hard [Storer and Szymanski 1982], and many heuristics have been proposed [Lynch 1973; Mayne and 3 James 1975; Rubin 1976; Schuegraf and Heaps 1973; Wagner 1973; White 1967; Wolff 1978] The novelty of the approach presented here is in the heuristic used for selecting digrams for replacement and the entropy coding method. The ....

Storer, J. A. and T. G. Szymanski, "Data compression via textual substitution," J. ACM 29 (4), October 1982, pp. 928-951.

....in the future. They theoretically perform well, that is, the performance achieved by them is asymptotically optimal, but practically convergence of the performance is slow. They were not used for reason of practical bad performance, but the variations of them are widely used, for example LZSS [10], LZW [11] LZFG [4] etc. The LZW code is used in the compress command and in modem protocol by its speed, good performance and easiness of implementation. The compression speed of the LZSS code is slower than the LZW, therefore it was not used too much in those days. However, its decompression ....

J. A. Storer and T. G. Szymanski. Data compression via textual substitution. Journal of the ACM, 29(4):928--951, 1982.

....techniques could show this approach to be optimal, we can work around the potential problem of optimality by processing data in blocks. On each block, we perform an optimal parse (e.g. using dynamic programming from right to left in the block along the lines of Storer and Szymanski [1978, 1982] [32,33] see also the book of Storer [29] The optimal parse of the joint compression uses the same or fewer bits as the individual compression of the block. The only added cost is when a pointer of the individual compression overlaps a block boundary and is charged to two blocks in this analysis; ....

J. Storer, T. Szymanski, Data compression via textual substitution, Journal of the Association for Computing Machinery 29 (4) (1982) 928 951.

....identify matches in previously seen text) to lossless image compression. We examine complexity issues and finish by considering practical 2 D implementations for bi level images. Received July 1, 1996; revised February 15, 1997 1. INTRODUCTION Ziv and Lempel [1, 2] and Storer and Szymanski [3, 4] introduced the notion of compressing text using methods that replace a substring of text by a pointer to an earlier occurrence. LZ1 (also called LZ 77) is a term often used to refer to a wide class of methods based on the basic principle presented in [1] where, as depicted in Figure 1, a ....

....by a displacement length reference to a string previously seen in the text (a pointer is a pair of integer values) Ziv and Lempel [1] proposed sending an uncoded character with every pointer, which ensures that progress is always made even when a match cannot be found. Storer and Szymanski [3, 4] and most practical methods usually either flag raw characters or reserve a pointer value for each character. Because a pointer has two fields (displacement and length) a fixed length code is unlikely to optimally partition bits between the two fields; in addition, the length field is typically ....

[Article contains additional citation context not shown here]

Storer, J. A. and Szymanski, T. G. (1982) Data compression via textual substitution. J. ACM, 29, 928--951.

....techniques could show this approach to be optimal, we can work around the potential problem of optimality by processing data in blocks. On each block, we perform an optimal parse (e.g. using dynamic programming from right to left in the block along the lines of Storer and Szymanski [SS 78, SS 82] see also the book of Storer [S 88] The optimal parse of the joint compression uses the same or fewer bits as the individual compression of the block. The only added cost is when a pointer of the individual compression overlaps a block boundary and is charged to two blocks in this analysis; ....

J. Storer and T. Szymanski, Data Compression Via Textual Substitution, JACM, 29:4, 928--951. (1982).

....of D and the current match. Textual substitution methods are often referred to as LZ type methods due to the work of Lempel and Ziv [1976] and Ziv and Lempel [1977,1978] where LZ1 type or LZ 77 type methods are those based on matching to the preceding n characters and LZ2type (see also Storer and Szymanski [1978,1982]) or LZ 78 type are those based on a dynamic dictionary, usually represented by a trie data structure in practice. For example, the UNIX gzip utility employs the LZ77 approach and the UNIX compress utility as well as the V.42bis modem compression standard employs the LZ78 approach. For ....

J. A. Storer and T. Szymanski [1982]. "Data Compression Via Textual Substitution", Journal of the ACM 29:4 928-951.

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J. A. Storer and T. G. Szymanski. Data Compression via Textual Substitution. Journal of the ACM, 29:928--951, 1982.

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Storer J.A., Szymanski, T.G., Data compression via textual substitution, Journal of the ACM 29 (1982) 928--951.

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J. A. Storer amd T. G. Syzmanski. Data compression via textual substitution. Journal of the ACM, 29, 1982.

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Storer, J., and Szymanski, T. Data compression via textual substitution. Jour. ACM 49, 4 (October 1982), 928--951.

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Storer, J. A. & Szymanski, T. G. (1982). Data compression via textual substitution. Journal of the ACM, 29:928-951.

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J. A. Storer and T. G. Szymanski. Data compression via textual substitution. Journal of the ACM, 29(4):928--951, 1982.

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J. Storer and T.G. Szymanski. Data compression via textual substitution. Journal of the ACM, 29:928-951, 1982.

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J. Storer and T. Szymanski. Data compression via textual substitution. J. Assoc. Comput. Mach., 29(4):928-951, 1982.

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J. Storer and T.G. Szymanski. Data compression via textual substitution. Journal of the ACM, 29:928-951, 1982.

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J. A. Storer and T. G. Szymanski, \Data compression via textual substitution", Journal of ACM, vol. 29, No. 4, pp. 928-951, October 1982.

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J. A. Storer and T. G. Szymanski, `Data compression via textual substitution', J ACM, 29, (4), 928-- 951 (1982).

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J. A. Storer and T. Szymanski. Data Compression via Textual Substitution. J.ACM, 1982.

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Storer, J. A. 85 Szymanski, T. G. (1982). Data compression via textual substitution. Journal of the ACM, 29:928-951.

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J.A. Storer, T.G. Szymanski, "Data compression via textual substitution", J. ACM, Vol. 29, No. 4, Oct. 1982, pp. 928--951.

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Storer J.A., Szymanski, T.G. (1982), Data compression via textual substitution, J. ACM 29 928--951.

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SS82: Storer, J.A., Szymanski, T.G., Data compression via textual substitution, J.ACM 29, 4, (1982) 928-951.

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