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41
SpaceEfficient Preprocessing Schemes for Range Minimum Queries on Static Arrays
, 2009
"... Given a static array of n totally ordered object, the range minimum query problem is to build an additional data structure that allows to answer subsequent online queries of the form “what is the position of a minimum element in the subarray ranging from i to j? ” efficiently. We focus on two sett ..."
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Cited by 47 (3 self)
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Given a static array of n totally ordered object, the range minimum query problem is to build an additional data structure that allows to answer subsequent online queries of the form “what is the position of a minimum element in the subarray ranging from i to j? ” efficiently. We focus on two settings, where (1) the input array is available at query time, and (2) the input array is only available at construction time. In setting (1), we show new data structures (a) of n c(n) (2 + o(1)) bits and query time O(c(n)), or (b) with O(nHk) + o(n) bits and O(1) query size time, where Hk denotes the empirical entropy of k’th order of the input array. In setting (2), we give a data structure of optimal size 2n + o(n) bits and query time O(1). All data structures can be constructed in linear time and almost inplace.
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 35 (17 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
Colored Range Queries and Document Retrieval
"... Colored range queries are a wellstudied topic in computational geometry and database research that, in the past decade, have found exciting applications in information retrieval. In this paper we give improved time and space bounds for three important onedimensional colored range queries — colore ..."
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Cited by 32 (18 self)
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Colored range queries are a wellstudied topic in computational geometry and database research that, in the past decade, have found exciting applications in information retrieval. In this paper we give improved time and space bounds for three important onedimensional colored range queries — colored range listing, colored range topk queries and colored range counting — and, thus, new bounds for various document retrieval problems on general collections of sequences. Specifically, we first describe a framework including almost all recent results on colored range listing and document listing, which suggests new combinations of data structures for these problems. For example, we give the fastest compressed data structures for colored range listing and document listing, and an efficient data structure for document listing whose size is bounded in terms of the highorder entropies of the library of documents. We then show how (approximate) colored topk queries can be reduced to (approximate) rangemode queries on subsequences, yielding the first efficient data structure for this problem. Finally, we show how a modified wavelet tree can support colored range counting in logarithmic time and space that is succinct whenever the number of colors is superpolylogarithmic in the length of the sequence.
Topk document retrieval in optimal time and linear space
 In Proc. 22nd Annual ACMSIAM Symposium on Discrete Algorithms (SODA 2012
, 2012
"... We describe a data structure that uses O(n)word space and reports k most relevant documents that contain a query pattern P in optimal O(P  + k) time. Our construction supports an ample set of important relevance measures, such as the frequency of P in a document and the minimal distance between t ..."
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Cited by 29 (17 self)
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We describe a data structure that uses O(n)word space and reports k most relevant documents that contain a query pattern P in optimal O(P  + k) time. Our construction supports an ample set of important relevance measures, such as the frequency of P in a document and the minimal distance between two occurrences of P in a document. We show how to reduce the space of the data structure from O(n log n) to O(n(log σ+log D+log log n)) bits, where σ is the alphabet size and D is the total number of documents. 1
Practical Compressed Document Retrieval
"... Recent research on document retrieval for general texts has established the virtues of explicitly representing the socalled document array, which stores the document each pointer of the suffix array belongs to. While it makes document retrieval faster, this array occupies a significative amount of ..."
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Cited by 20 (16 self)
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Recent research on document retrieval for general texts has established the virtues of explicitly representing the socalled document array, which stores the document each pointer of the suffix array belongs to. While it makes document retrieval faster, this array occupies a significative amount of redundant space and is not easily compressible. In this paper we present the first practical proposal to compress the document array. We show that the resulting structureis significatively smaller than the uncompressed counterpart, and than alternatives to the document array proposed in the literature. We also compare various known algorithms for document listing and topk retrieval, and find that the most useful combinations of algorithms run over our new compressed document arrays.
Improved compressed indexes for fulltext document retrieval
 IN PROC. 18TH SPIRE
, 2011
"... We give new space/time tradeoffs for compressed indexes that answer document retrieval queries on general sequences. On a collection of D documents of total length n, current approaches require at lg D lg lg D least CSA  + O(n) or 2CSA  + o(n) bits of space, where CSA is a fulltext index. Usin ..."
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Cited by 18 (10 self)
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We give new space/time tradeoffs for compressed indexes that answer document retrieval queries on general sequences. On a collection of D documents of total length n, current approaches require at lg D lg lg D least CSA  + O(n) or 2CSA  + o(n) bits of space, where CSA is a fulltext index. Using monotone minimum perfect hash functions, we give new algorithms for document listing with frequencies and topk document retrieval using just CSA  + O(n lg lg lg D) bits. We also improve current solutions that use 2CSA  + o(n) bits, and consider other problems such as colored range listing, topk most important documents, and computing arbitrary frequencies.
Spaces, trees and colors: The algorithmic landscape of document retrieval on sequences
 CoRR
"... Document retrieval is one of the best established information retrieval activities since the sixties, pervading all search engines. Its aim is to obtain, from a collection of text documents, those most relevant to a pattern query. Current technology is mostly oriented to “natural language” text coll ..."
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Cited by 14 (9 self)
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Document retrieval is one of the best established information retrieval activities since the sixties, pervading all search engines. Its aim is to obtain, from a collection of text documents, those most relevant to a pattern query. Current technology is mostly oriented to “natural language” text collections, where inverted indexes are the preferred solution. As successful as this paradigm has been, it fails to properly handle various East Asian languages and other scenarios where the “natural language ” assumptions do not hold. In this survey we cover the recent research in extending the document retrieval techniques to a broader class of sequence collections, which has applications in bioinformatics, data and Web mining, chemoinformatics, software engineering, multimedia information retrieval, and many other fields. We focus on the algorithmic aspects of the techniques, uncovering a rich world of relations between document retrieval challenges and fundamental problems on trees, strings, range queries, discrete geometry, and other areas.
SpaceEfficient Topk Document Retrieval
"... Supporting topk document retrieval queries on general text databases, that is, finding the k documents where a given pattern occurs most frequently, has become a topic of interest with practical applications. While the problem has been solved in optimal time and linear space, the actual space usag ..."
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Cited by 14 (8 self)
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Supporting topk document retrieval queries on general text databases, that is, finding the k documents where a given pattern occurs most frequently, has become a topic of interest with practical applications. While the problem has been solved in optimal time and linear space, the actual space usage is a serious concern. In this paper we study various reducedspace structures that support topk retrieval and propose new alternatives. Our experimental results show that our novel structures and algorithms dominate almost all the space/time tradeoff.
TopK color queries for document retrieval
, 2010
"... In this paper we describe a new efficient (in fact optimal) data structure for the topK color problem. Each element of an array A is assigned a color c with priority p(c). For a query range [a, b] and a value K, we have to report K colors with the highest priorities among all colors that occur in A ..."
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Cited by 14 (3 self)
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In this paper we describe a new efficient (in fact optimal) data structure for the topK color problem. Each element of an array A is assigned a color c with priority p(c). For a query range [a, b] and a value K, we have to report K colors with the highest priorities among all colors that occur in A[a..b], sorted in reverse order by their priorities. We show that such queries can be answered in O(K) time using an O(N log σ) bits data structure, where N is the number of elements in the array and σ is the number of colors. Thus our data structure is asymptotically optimal with respect to the worstcase query time and space. As an immediate application of our results, we obtain optimal time solutions for several document retrieval problems. The method of the paper could be also of independent interest.
Compressed selfindices supporting conjunctive queries on document collections
 in: Proc. 17th SPIRE, 2010
"... Abstract. We prove that a document collection, represented as a unique sequence T of n terms over a vocabulary Σ, can be represented in nH0(T) + o(n)(H0(T) + 1) bits of space, such that a conjunctive query t1 ∧ · · · ∧ tk can be answered in O(kδ log log Σ) adaptive time, where δ is the instanc ..."
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Cited by 12 (1 self)
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Abstract. We prove that a document collection, represented as a unique sequence T of n terms over a vocabulary Σ, can be represented in nH0(T) + o(n)(H0(T) + 1) bits of space, such that a conjunctive query t1 ∧ · · · ∧ tk can be answered in O(kδ log log Σ) adaptive time, where δ is the instance difficulty of the query, as defined by Barbay and Kenyon in their SODA’02 paper, and H0(T) is the empirical entropy of order 0 of T. As a comparison, using an inverted index plus the adaptive intersection algorithm by Barbay and Kenyon takes O(kδ log nM δ), where nM is the length of the shortest and longest occurrence lists, respectively, among those of the query terms. Thus, we can replace an inverted index by a more spaceefficient inmemory encoding, outperforming the query performance of inverted indices when the ratio nM δ is ω(log Σ).