A. Amir, G. Benson, Efficient two-dimensional compressed matching, Processings of Data Compression Conference, DCC'92, Snowbird, Utah, 1992, pp.279-288.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....pattern matching, LZ family com pression, mutiple pattern, 1 Introduction Recently, the compressed pattern matching problem has attracted special concern where the goal is to find a pattern in a compressed text without decompressing it. The problem was first defined by Amir and Benson [3], and several researchers have tackled this problem for various compression methods (see an, excellent survey paper [23] Amir, Benson, and Farach[4] addressed the LZW compression[27] and presented a series of algorithms having various time and space complexities (O(n rn 2) time and space, ....

A. Amir and G. Benson. Efficient two-dimensional compressed matching. In Proc. Data Compression Conference, page 279, 1992.

....are often stored in compressed forms. We therefore need a fast pattern matching technique for searching the compressed text directly. Several researchers tackled this problem. Eilam Tsoreff and Vishkin[6] addressed the run length compression, and Amir, Landau, and Vishikin[5] and Amir and Benson[2, 3] addressed its twodimensional version. Farach and Thorup[7] and Gasieniec, et al. 8] addressed the LZ77 compression[14] Amir, Benson, and Farach[4] addressed the LZW compression[13] Karpinski, et al. 9] and Miyazaki, et al. 12] addressed the straight line programs. For a fast pattern matching ....

A. Amir and G. Benson. Efficient two-dimensional compressed matching. In Proc. Data Compression Conference, page 279, 1992.

....searches can be performed almost at the same search cost of simple searches. Moreover, the reduced I O to read the compressed text makes this algorithm even faster than those that work on plain uncompressed text. The compressed matching problem was first defined in the work of Amir and Benson [1] as the task of performing string matching in a compressed text without decompressing it. Giving a text T , a corresponding compressed string Z, and a pattern P , the compressed matching problem consists in finding all occurrences of P in T , using only P and Z. A naive algorithm, which first ....

A. Amir and G. Benson. Efficient two-dimensional compressed matching. In Proc. Second IEEE Data Compression Conference, pages 279--288, March 1992.

....In other words, the text compression can speed up the pattern matching. In this framework, it is required to develop an efficient pattern matching algorithm for searching directly the compressed text without decoding. The compressed pattern matching problem has been studied by many researchers [6, 5, 1, 2, 3, 7, 9, 4, 10, 13, 11], mainly from theoretical viewpoints. Most of the compression methods dealt with are the adaptive compression methods such as the LZ77 compression [15] and the LZW compression [14] Since in such compression methods the encoding of text substring depends on the previous part of the text, it is ....

A. Amir and G. Benson. Efficient two-dimensional compressed matching. In Proc. Data Compression Conference, page 279, 1992.

....compression and indexing of data collections. The exploitation of data compressibility have been already investigated only with respect to its impact on algorithmic performance in the context of on line algorithms (e.g. caching and prefetching [15, 17] string matching algorithms (see e.g. [1, 2, 9]) sorting and computational geometry algorithms [8] The scenario. Most of the research in the design of indexing data structures has been directed to devise solutions which offer a good trade off between query and update time versus space usage. The two main approaches are wordbased indices ....

....decreases the demand of storage at the expenses of processing, it is becoming more economical to store data in a compressed form rather than uncompressed. Starting from these promising considerations, many researchers have recently concentrated on the compressed matching problem, introduced in [1], as the task of performing string matching in a compressed text without decompressing it. A collection of algorithms is currently known to solve efficiently (possibly optimally) this problem on text compressed by means of various schemes: e.g. run length [1] LZ77 [9] LZ78 [2] Huffman [24] All ....

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A. Amir and G. Benson. Efficient two-dimensional compressed matching. Proceedings of IEEE Data Compression Conference, pages 279--288, 1992.

....[ZL77, ZL78] is one of the most popular in practice because of their good compression ratios combined with efficient compression and decompression time. It is natural to think of merging search and compression. The compressed matching problem was first defined in the work of Amir and Benson [AB92] as the task of performing string matching in a compressed text without decompressing it. Given a text T , a corresponding compressed string Z = z 1 : z n , and a pattern P , the compressed matching problem consists in finding all occurrences of P in T , using only P and Z. A naive algorithm, ....

....of having a searchable and compressed text are not easy to achieve together, as the only solution before the 90 s was to process queries by uncompressing the texts and then searching into them. In particular, approximate searching on compressed text was advocated in 1992 as an open problem [AB92] Only very recently a couple of solutions have appeared [KNU00, MKT 00] Despite their theoretical achievements, which are nontrivial, the experimental results in both papers show that in practice they are slower than a decompression of the text followed by a state of the art search on the ....

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A. Amir and G. Benson. Efficient two-dimensional compressed matching. In Proc. DCC'92, pages 279--288, 1992.

....The idea is in this sense similar to that of Watson, but takes less space. The search method is also different: instead of a Boyer Moore like algorithm, it is based on BNDM [23] 2. 2 Compressed Pattern Matching The compressed matching problem was first defined in the work of Amir and Benson [2] as the task of performing string matching in a compressed text without decompressing it. Given a text T , a corresponding compressed string Z = z 1 : z n , and a pattern P , the compressed matching problem consists in finding all occurrences of P in T , using only P and Z. A naive algorithm, ....

....[12] Recently, Navarro and Tarhio [25] presented a new, faster, algorithm based on Boyer Moore. Approximate string matching on compressed text aims at finding the pattern where a limited number of differences between the pattern and its occurrences are permitted. The problem, advocated in 1992 [2], had been solved for Huffman coding of words [18] but the solution is limited to search a whole word and retrieve whole words that are similar. The first true solutions appeared very recently, by Karkkainen et al. 11] Matsumoto et al. 16] and Navarro et al. 22] 3 The Ziv Lempel Compression ....

A. Amir and G. Benson. Efficient two-dimensional compressed matching. In Proc. DCC'92, pages 279--288, 1992.

....are many different compression schemes, among which the Ziv Lempel family [23, 24] is one of the best in practice because of their good compression ratios combined with efficient compression and decompression time. The compressed matching problem was first defined in the work of Amir and Benson [1] as the task of performing string matching in a compressed text without decompressing it. Given a text T , a corresponding compressed string Z = z 1 : z n , and a pattern P , the compressed matching problem consists in finding all occurrences of P in T , using only P and Z. A naive algorithm, ....

A. Amir and G. Benson. Efficient two-dimensional compressed matching. In Proc. DCC'92, pages 279--288, 1992.

....are many different compression schemes, among which the Ziv Lempel family [23, 24] is one of the best in practice because of their good compression ratios combined with efficient compression and decompression time. The compressed matching problem was first defined in the work of Amir and Benson [1] as the task of performing string matching in a compressed text without decompressing it. Given a text T , a corresponding compressed string Z = z 1 : z n , and a pattern P , the compressed matching problem consists in finding all occurrences of P in T , using only P and Z. A naive algorithm, ....

....be efficiently searched. Surprisingly, these two combined requirements are not easy to achieve together, as the only solution before the 90 s was to process queries by uncompressing the texts and then searching into them. In particular, approximate searching on compressed text was advocated in [1] as an open problem. This is the problem we solve in this paper: we present the first solution for compressed approximate string matching. The format we choose is the ZivLempel family, focusing in the LZ78 and LZW variants. By modifying the basic dynamic programming algorithm, we achieve a time ....

A. Amir and G. Benson. Efficient two-dimensional compressed matching. In Proc. DCC'92, pages 279--288, 1992.

....we present a new technique to search for patterns on compressed texts, where the patterns are compressed and the search is processed without any decoding of the compressed text. EXTEND AND DETAIL THIS PARAGRAPH. The compressed matching problem was first defined in the work of Amir and Benson [AB92] as the task of performing string matching in a compressed text without decompressing it. Giving a text T , a corresponding compressed string Z, and a pattern P , the compressed matching problem consists in finding all occurrences of P in T , using only P and Z. A naive algorithm, which first ....

A. Amir and G. Benson. Efficient two-dimensional compressed matching. Proc. Second IEEE Data Compression Conference, pages 279--288, Mar. 1992.

....x Instytut Informatyki, Uniwersytet Warszawski, Banacha 2, 02 097 Warszawa, Poland. Supported partially by the grant KBN 8T11C01208. Email:rytter mimuw.edu.pl 1 Introduction In the algorithmics of textual problems only recently the problems related to compressed objects were investigated ( 1] [2], 3] and [8] A very natural way and practical method of the text compression is the LZ compression (see [12] In this paper we consider several problems for LZ compressed strings: pattern matching and computation of all periods, palindromes and squares of a given compressed string (without ....

A.Amir, G. Benson, Efficient two dimensional compressed matching, Proc. of the 2nd IEEE Data Compression Conference 279-288 (1992) 7

....University of Chile. Blanco Encalada 2120, Santiago, Chile. gnavarro dcc.uchile.cl y Institut Gaspard Monge, Cit e Descartes, Champs sur Marne, 77454 Marne la Vall ee Cedex 2, France. raffinot monge.univ mlv.fr 1 The compressed matching problem was first defined in the work of Amir and Benson [1] as the task of performing string matching in a compressed text without decompressing it. Giving a text T , a corresponding compressed string Z = z 1 : z n , and a pattern P , the compressed matching problem consists in finding all occurrences of P in T , using only P and Z. A naive algorithm, ....

A. Amir and G. Benson. Efficient two-dimensional compressed matching. In Proc. Second IEEE Data Compression Conference, pages 279--288, March 1992.

....be efficiently searched. Surprisingly, these two combined requirements are not easy to achieve together, as the only solution before the 90 s was to process queries by uncompressing the texts and then searching into them. The compressed matching problem was first defined by Amir and Benson [1] as the task of performing string matching in a compressed text without decompressing it. Given a text T , a corresponding compressed string Z = z 1 : z n , and a pattern P , the compressed matching problem consists in finding all occurrences of P in T , using only P and Z. A naive algorithm, ....

A. Amir and G. Benson. Efficient two-dimensional compressed matching. In Proc. Second IEEE Data Compression Conference, pages 279--288, March 1992.

....The elimination of repetition is the key to compression. Intuitively, once a string has been compressed and therefore its repetitive nature has been elucidated one might be tempted to exploit this knowledge to speed up string matching. This idea is inherent in the work of Amir and Benson [2], where they introduced the Compressed Matching Problem. They were motivated by the practical consideration that, increasingly, files are stored in a compressed format, and that current string matching technology requires the files be uncompressed before string matching takes place. The ....

....a constant factor of optimal, schemes such as LZ2 and LZW can deviate from optimality by an exponential factor. 1.1 PREVIOUS RESULTS The theory of compressed matching was initiated with the study of two dimensions run length compression, the compression algorithm used for fax transitions. In [2, 4], an optimal O(n p 2 ) algorithm was derived for finding a p Theta p two dimensional pattern within a file of length n. In one dimension, perhaps the most commonly used compression algorithm is the LZW algorithm [15] as implemented by the UNIX compress program [14] In [3] it was shown ....

A. Amir and G. Benson. Efficient two dimensional compressed matching. Proc. of the 2nd IEEE Data Compression Conference, pages 279--288, Mar 1992.

....be kept in compressed form. With these large amounts of compressed data in computer archives, the need arises to process the data in it s compressed form. Here, processing implies complex operations, such as spatial searches in compressed raster images [15] or pattern matching in compressed files [2, 3, 9]. More details about the role of complex operations in a variety of settings is illustrated in the IEEE Computer special issue on Finding the Right Image [10] For satellite images, we want to be able to quickly match a (small) raster image with a (large) two dimensional compressed raster image; ....

....we want to be able to quickly match a (small) raster image with a (large) two dimensional compressed raster image; let us call this the two dimensional compressed pattern matching problem. This problem has been studied for the case in which runlength compression has been applied to the image [2]. In our experience, however, run length compression is not the method of choice for satellite images; prefix codes such as Huffman s seem to be more efficient in terms of compression ratio and are already used in state of the art compression methods [11, 14] In this paper, we propose a ....

A. Amir and G. Benson. Efficient two-dimensional compressed matching. In J. A. Storer and J. H. Reif, editors, Data Compression Conference, pages 279--288. IEEE, Mar. 24 - 27 1992. Snowbird, Utah.

....developments in multimedia have led to a vast increase in the amount of stored data. This increase has made it critically important to store and transmit files in a compressed form. The need to quickly access this data has given rise to a new paradigm in searching, that of compressed matching [1, 5, 6]. In traditional pattern matching, the pattern (P ) and text (T ) are explicitly given, and all occurrences of P in T are sought. In compressed pattern matching the goal is the same, however, the pattern and text are given in compressed form. Let c be a compression algorithm, and let c(D) be the ....

....locations in T of sharp occurrences of P . Formally, the output is the set of locations (i; j) such that T [i k; j l] P [k 1; l 1] k; l = 0 : m Gamma 1, and T [i k; j] 6= T [i k; j Gamma 1] T [i k; j m Gamma 1] 6= T [i k; j m] k = 0 : m Gamma 1. Amir and Benson [1] presented an algorithm that solves this problem 1 in time O(jc(T )j log jc(T )j) The authors then improved this algorithm in [3] achieving an algorithm that has both time and space O(jc(T )j) Using known techniques, it is possible to modify the AmirBenson Farach algorithm [3] so that its ....

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A. Amir and G. Benson. Efficient two dimensional compressed matching. Proc. of Data Compression Conference, Snow Bird, Utah, pages 279--288, Mar 1992.

....two dimensional tool, that of two dimensional periodicity. The two dimensional periodicity idea has been instrumental in several interesting two dimensional results. Amir, Benson and Farach [3] introduced the first alphabet independent two dimensional text scanning algorithm. Amir and Benson [1] gave an algorithm that searches for appearances of a two dimensional pattern in a compressed text. Amir, Benson, and Farach [4] gave the first optimal parallel CREW two dimensional text scanning algorithm. This was followed by Muthukrishnan and Ramesh [13] and, independently, Crochemore, ....

A. Amir and G. Benson. Efficient two dimensional compressed matching. Proc. of Data Compression Conference, Snow Bird, Utah, pages 279--288, Mar 1992.

....The scaled matching problem was studied for the first time by Amir, Landau and Vishkin [11] They showed that all appearances in text T of a pattern P scaled to any discrete size, can be found in linear time for fixed finite alphabets. That solution gave rise to the compressed matching problem [2, 7] which, in turn led to the development of two dimensional periodicity [3] Two dimensional periodicity turned out to be the most important tool in two dimensional matching. Its development led to an alphabet independent two dimensional matching algorithm [6, 4, 18] and to optimal parallel two ....

A. Amir and G. Benson. Efficient two dimensional compressed matching. Proc. of Data Compression Conference, Snow Bird, Utah, pages 279--288, Mar 1992.

....that the compression achieve a good ratio and that the compression algorithm be fast. We now need algorithms for pattern matching in time and space proportional to the compressed size, i.e. without the need to decompress. The compressed matching problem was formally defined by Amir and Benson [2, 1] as follows: Let oe = s 1 1 1 1 s u be a text string of length u over alphabet 6 = fa 1 ; a q g. Let oe:c = t 1 1 1 1 t n be a compression of oe of length n u. INPUT: Compressed text oe:c = t 1 1 1 1 t n , and pattern P = p 1 1 1 1 pm . OUTPUT: The first text location i such that ....

....: a q g. Let oe:c = t 1 1 1 1 t n be a compression of oe of length n u. INPUT: Compressed text oe:c = t 1 1 1 1 t n , and pattern P = p 1 1 1 1 pm . OUTPUT: The first text location i such that there is a pattern occurrence at s i , i.e. s i j01 = p j ; j = 1; m. Amir and Benson [2, 1] also defined a compressed matching to be efficient if its time complexity is o(u) almost optimal if its time complexity is O(n log m m) and optimal if it runs in time O(n m) The first compressed matching algorithms were side effects of papers by Eilam Tsoreff and Vishkin [6] and Amir, Landau ....

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A. Amir and G. Benson. Efficient two dimensional compressed matching. Proc. of Data Compression Conference, Snow Bird, Utah, pages 279--288, Mar 1992.

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A. Amir, G. Benson, Efficient two-dimensional compressed matching, Processings of Data Compression Conference, DCC'92, Snowbird, Utah, 1992, pp.279-288.

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Amihood Amir and Gary Benson. Efficient two-dimensional compressed matching. In James A. Storer and John H. Reif, editors, Proc. Data Compression Conference, pages 279--288. IEEE, 1992.

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A. Amir, G. Benson, Efficient two dimensional compressed matching, Proceedings of the 2 IEEE Data Compression Conference, pp. 279--288 (1992).

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A. Amir and G. Benson, Efficient two dimensional compressed matching, Proc. of the 2nd IEEE Data Compression Conference 279-288 (1992).

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A. Amir, G. Benson, Efficient two dimensional compressed matching, Proc. of the 2nd IEEE Data Compression Conference 279-288 (1992).

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A. Amir and G. Benson, Efficient two dimensional compressed matching, Proc. of 2nd IEEE Data Compression Conference, pp. 279--288, March 1992.

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