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103
Compressed fulltext indexes
 ACM COMPUTING SURVEYS
, 2007
"... Fulltext indexes provide fast substring search over large text collections. A serious problem of these indexes has traditionally been their space consumption. A recent trend is to develop indexes that exploit the compressibility of the text, so that their size is a function of the compressed text l ..."
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Cited by 173 (78 self)
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Fulltext indexes provide fast substring search over large text collections. A serious problem of these indexes has traditionally been their space consumption. A recent trend is to develop indexes that exploit the compressibility of the text, so that their size is a function of the compressed text length. This concept has evolved into selfindexes, which in addition contain enough information to reproduce any text portion, so they replace the text. The exciting possibility of an index that takes space close to that of the compressed text, replaces it, and in addition provides fast search over it, has triggered a wealth of activity and produced surprising results in a very short time, and radically changed the status of this area in less than five years. The most successful indexes nowadays are able to obtain almost optimal space and search time simultaneously. In this paper we present the main concepts underlying selfindexes. We explain the relationship between text entropy and regularities that show up in index structures and permit compressing them. Then we cover the most relevant selfindexes up to date, focusing on the essential aspects on how they exploit the text compressibility and how they solve efficiently various search problems. We aim at giving the theoretical background to understand and follow the developments in this area.
Spaceefficient algorithms for document retrieval
 IN PROC. CPM, VOLUME 4580 OF LNCS
, 2007
"... We study the Document Listing problem, where a collection D of documents d1,..., dk of total length � di = n is to be prei processed, so that one can later efficiently list all the ndoc documents containing a given query pattern P of length m as a substring. Muthukrishnan (SODA 2002) gave an opti ..."
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Cited by 34 (2 self)
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We study the Document Listing problem, where a collection D of documents d1,..., dk of total length � di = n is to be prei processed, so that one can later efficiently list all the ndoc documents containing a given query pattern P of length m as a substring. Muthukrishnan (SODA 2002) gave an optimal solution to the problem; with O(n) time preprocessing, one can answer the queries in O(m + ndoc) time. In this paper, we improve the spacerequirement of the Muthukrishnan’s solution from O(nlog n) bits to CSA  + 2n + nlog k(1 + o(1)) bits, where CSA  ≤ nlog Σ(1 + o(1)) is the size of any suitable compressed suffix array (CSA), and Σ is the underlying alphabet of documents. The time requirement depends on the CSA used, but we can obtain e.g. the optimal O(m+ndoc) time when Σ, k = O(polylog(n)). For general Σ, k the time requirement becomes O(m log Σ  + ndoc log k). Sadakane (ISAAC
Rank and select revisited and extended
 Workshop on SpaceConscious Algorithms, University of
, 2006
"... The deep connection between the BurrowsWheeler transform (BWT) and the socalled rank and select data structures for symbol sequences is the basis of most successful approaches to compressed text indexing. Rank of a symbol at a given position equals the number of times the symbol appears in the corr ..."
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Cited by 33 (17 self)
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The deep connection between the BurrowsWheeler transform (BWT) and the socalled rank and select data structures for symbol sequences is the basis of most successful approaches to compressed text indexing. Rank of a symbol at a given position equals the number of times the symbol appears in the corresponding prefix of the sequence. Select is the inverse, retrieving the positions of the symbol occurrences. It has been shown that improvements to rank/select algorithms, in combination with the BWT, turn into improved compressed text indexes. This paper is devoted to alternative implementations and extensions of rank and select data structures. First, we show that one can use gap encoding techniques to obtain constant time rank and select queries in essentially the same space as what is achieved by the best current direct solution (and sometimes less). Second, we extend symbol rank and select to substring rank and select, giving several space/time tradeoffs for the problem. An application of these queries is in positionrestricted substring searching, where one can specify the range in the text where the search is restricted to, and only occurrences residing in that range are to be reported. In addition, arbitrary occurrences are reported in text position order. Several byproducts of our results display connections with searchable partial sums, Chazelle’s twodimensional data structures, and Grossi et al.’s wavelet trees.
Practical rank/select queries over arbitrary sequences
 In Proc. 15th SPIRE, LNCS 5280
, 2008
"... Abstract. We present a practical study on the compact representation of sequences supporting rank, select, and access queries. While there are several theoretical solutions to the problem, only a few have been tried out, and there is little idea on how the others would perform, especially in the cas ..."
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Cited by 32 (23 self)
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Abstract. We present a practical study on the compact representation of sequences supporting rank, select, and access queries. While there are several theoretical solutions to the problem, only a few have been tried out, and there is little idea on how the others would perform, especially in the case of sequences with very large alphabets. We first present a new practical implementation of the compressed representation for bit sequences proposed by Raman, Raman, and Rao [SODA 2002], that is competitive with the existing ones when the sequences are not too compressible. It also has nice local compression properties, and we show that this makes it an excellent tool for compressed text indexing in combination with the BurrowsWheeler transform. This shows the practicality of a recent theoretical proposal [Mäkinen and Navarro, SPIRE 2007], achieving spaces never seen before. Second, for general sequences, we tune wavelet trees for the case of very large alphabets, by removing their pointer information. We show that this gives an excellent solution for representing a sequence within zeroorder entropy space, in cases where the large alphabet poses a serious challenge to typical encoding methods. We also present the first implementation of Golynski et al.’s representation [SODA 2006], which offers another interesting time/space tradeoff. 1
Implicit compression boosting with applications to selfindexing
 In Proc. SPIRE'07, LNCS 4726
, 2007
"... Abstract. Compression boosting (Ferragina & Manzini, SODA 2004) is a new technique to enhance zeroth order entropy compressors ’ performance to kth order entropy. It works by constructing the BurrowsWheeler transform of the input text, finding optimal partitioning of the transform, and then compre ..."
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Cited by 29 (16 self)
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Abstract. Compression boosting (Ferragina & Manzini, SODA 2004) is a new technique to enhance zeroth order entropy compressors ’ performance to kth order entropy. It works by constructing the BurrowsWheeler transform of the input text, finding optimal partitioning of the transform, and then compressing each piece using an arbitrary zeroth order compressor. The optimal partitioning has the property that the achieved compression is boosted to kth order entropy, for any k. The technique has an application to text indexing: Essentially, building a wavelet tree (Grossi et al., SODA 2003) for each piece in the partitioning yields a kth order compressed fulltext selfindex providing efficient substring searches on the indexed text (Ferragina et al., SPIRE 2004). In this paper, we show that using explicit compression boosting with wavelet trees is not necessary; our new analysis reveals that the size of the wavelet tree built for the complete BurrowsWheeler transformed text is, in essence, the sum of those built for the pieces in the optimal partitioning. Hence, the technique provides a way to do compression boosting implicitly, with a trivial linear time algorithm, but fixed to a specific zeroth order compressor (Raman et al., SODA 2002). In addition to having these consequences on compression and static fulltext selfindexes, the analysis shows that a recent dynamic zeroth order compressed selfindex (Mäkinen & Navarro, CPM 2006) occupies in fact space proportional to kth order entropy. 1
Range quantile queries: Another virtue of wavelet trees
 In Proc. 16th SPIRE, LNCS 5721
, 2009
"... Abstract. We show how to use a balanced wavelet tree as a data structure that stores a list of numbers and supports efficient range quantile queries. A range quantile query takes a rank and the endpoints of a sublist and returns the number with that rank in that sublist. For example, if the rank is ..."
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Cited by 27 (5 self)
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Abstract. We show how to use a balanced wavelet tree as a data structure that stores a list of numbers and supports efficient range quantile queries. A range quantile query takes a rank and the endpoints of a sublist and returns the number with that rank in that sublist. For example, if the rank is half the sublist’s length, then the query returns the sublist’s median. We also show how these queries can be used to support spaceefficient coloured range reporting and document listing. 1
SpaceEfficient Framework for Topk String Retrieval Problems
"... Given a set D = {d1, d2,..., dD} of D strings of total length n, our task is to report the “most relevant” strings for a given query pattern P. This involves somewhat more advanced query functionality than the usual pattern matching, as some notion of “most relevant” is involved. In information retr ..."
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Cited by 25 (3 self)
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Given a set D = {d1, d2,..., dD} of D strings of total length n, our task is to report the “most relevant” strings for a given query pattern P. This involves somewhat more advanced query functionality than the usual pattern matching, as some notion of “most relevant” is involved. In information retrieval literature, this task is best achieved by using inverted indexes. However, inverted indexes work only for some predefined set of patterns. In the pattern matching community, the most popular patternmatching data structures are suffix trees and suffix arrays. However, a typical suffix tree search involves going through all the occurrences of the pattern over the entire string collection, which might be a lot more than the required relevant documents. The first formal framework to study such kind of retrieval problems was given by Muthukrishnan [25]. He considered two metrics for relevance: frequency and proximity. He took a thresholdbased approach on these metrics and gave data structures taking O(n log n) words of space. We study this problem in a slightly different framework of reporting the top k most relevant documents (in sorted order) under similar and more general relevance metrics. Our framework gives linear space data structure with optimal query times for arbitrary score functions. As a corollary, it improves the space utilization for the problems in [25] while maintaining optimal query performance. We also develop compressed variants of these data structures for several specific relevance metrics.
Compressed Text Indexes with Fast Locate
"... Abstract. Compressed text (self)indexes have matured up to a point where they can replace a text by a data structure that requires less space and, in addition to giving access to arbitrary text passages, support indexed text searches. At this point those indexes are competitive with traditional tex ..."
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Cited by 24 (13 self)
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Abstract. Compressed text (self)indexes have matured up to a point where they can replace a text by a data structure that requires less space and, in addition to giving access to arbitrary text passages, support indexed text searches. At this point those indexes are competitive with traditional text indexes (which are very large) for counting the number of occurrences of a pattern in the text. Yet, they are still hundreds to thousands of times slower when it comes to locating those occurrences in the text. In this paper we introduce a new compression scheme for suffix arrays which permits locating the occurrences extremely fast, while still being much smaller than classical indexes. In addition, our index permits a very efficient secondary memory implementation, where compression permits reducing the amount of I/O needed to answer queries. 1 Introduction and Related Work Compressed text indexing has become a popular alternative to cope with the problem of giving indexed access to large text collections without using up too much space. Reducing space is important because it gives one the chance of maintaining the whole collection in main memory. The current trend in compressed indexing is fulltext compressed selfindexes [14, 1, 4, 15, 13, 2]. Such a selfindex (for short) replaces the
Topk Ranked Document Search in General Text Databases
"... Abstract. Text search engines return a set of k documents ranked by similarity to a query. Typically, documents and queries are drawn from natural language text, which can readily be partitioned into words, allowing optimizations of data structures and algorithms for ranking. However, in many new se ..."
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Cited by 22 (13 self)
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Abstract. Text search engines return a set of k documents ranked by similarity to a query. Typically, documents and queries are drawn from natural language text, which can readily be partitioned into words, allowing optimizations of data structures and algorithms for ranking. However, in many new search domains (DNA, multimedia, OCR texts, Far East languages) there is often no obvious definition of words and traditional indexing approaches are not so easily adapted, or break down entirely. We present two new algorithms for ranking documents against a query without making any assumptions on the structure of the underlying text. We build on existing theoretical techniques, which we have implemented and compared empirically with new approaches introduced in this paper. Our best approach is significantly faster than existing methods in RAM, and is even three times faster than a stateoftheart inverted file implementation for English text when word queries are issued. 1