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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 17 (9 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.
Alphabetindependent compressed text indexing
 In ESA
, 2011
"... Abstract. Selfindexes can represent a text in asymptotically optimal space under the kth order entropy model, give access to text substrings, and support indexed pattern searches. Their time complexities are not optimal, however: they always depend on the alphabet size. In this paper we achieve, f ..."
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Cited by 14 (10 self)
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Abstract. Selfindexes can represent a text in asymptotically optimal space under the kth order entropy model, give access to text substrings, and support indexed pattern searches. Their time complexities are not optimal, however: they always depend on the alphabet size. In this paper we achieve, for the first time, full alphabetindependence in the time complexities of selfindexes, while retaining space optimality. We obtain also some relevant byproducts on compressed suffix trees. 1
Wavelet Trees for All
"... The wavelet tree is a versatile data structure that serves a number of purposes, from string processing to geometry. It can be regarded as a device that represents a sequence, a reordering, or a grid of points. In addition, its space adapts to various entropy measures of the data it encodes, enabli ..."
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Cited by 10 (5 self)
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The wavelet tree is a versatile data structure that serves a number of purposes, from string processing to geometry. It can be regarded as a device that represents a sequence, a reordering, or a grid of points. In addition, its space adapts to various entropy measures of the data it encodes, enabling compressed representations. New competitive solutions to a number of problems, based on wavelet trees, are appearing every year. In this survey we give an overview of wavelet trees and the surprising number of applications in which we have found them useful: basic and weighted point grids, sets of rectangles, strings, permutations, binary relations, graphs, inverted indexes, document retrieval indexes, fulltext indexes, XML indexes, and general numeric sequences.
New lower and upper bounds for representing sequences
 CoRR
"... Abstract. Sequence representations supporting queries access, select and rank are at the core of many data structures. There is a considerable gap between different upper bounds, and the few lower bounds, known for such representations, and how they interact with the space used. In this article we p ..."
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Cited by 9 (8 self)
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Abstract. Sequence representations supporting queries access, select and rank are at the core of many data structures. There is a considerable gap between different upper bounds, and the few lower bounds, known for such representations, and how they interact with the space used. In this article we prove a strong lower bound for rank, which holds for rather permissive assumptions on the space used, and give matching upper bounds that require only a compressed representation of the sequence. Within this compressed space, operations access and select can be solved within almostconstant time. 1
Optimal Dynamic Sequence Representations
"... We describe a data structure that supports access, rank and select queries, as well as symbol insertions and deletions, on a string S[1, n] over alphabet [1..σ] in time O(lg n / lg lg n), which is optimal. The time is worstcase for the queries and amortized for the updates. This complexity is bette ..."
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Cited by 5 (3 self)
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We describe a data structure that supports access, rank and select queries, as well as symbol insertions and deletions, on a string S[1, n] over alphabet [1..σ] in time O(lg n / lg lg n), which is optimal. The time is worstcase for the queries and amortized for the updates. This complexity is better than the best previous ones by a Θ(1 + lg σ / lg lg n) factor. Our structure uses nH0(S) + O(n + σ(lg σ + lg 1+ε n)) bits, where H0(S) is the zeroorder entropy of S and 0 < ε < 1 is any constant. This space redundancy over nH0(S) is also better, almost always, than that of the best previous dynamic structures, o(n lg σ)+O(σ(lg σ+lg n)). We can also handle general alphabets in optimal time, which has been an open problem in dynamic sequence representations.
Improved grammarbased compressed indexes
 In Proc. 19th SPIRE, LNCS 7608
, 2012
"... Abstract. We introduce the first grammarcompressed representation of a sequence that supports searches in time that depends only logarithmically on the size of the grammar. Given a text T [1..u] that is represented by a (contextfree) grammar of n (terminal and nonterminal) symbols and size N (meas ..."
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Cited by 3 (2 self)
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Abstract. We introduce the first grammarcompressed representation of a sequence that supports searches in time that depends only logarithmically on the size of the grammar. Given a text T [1..u] that is represented by a (contextfree) grammar of n (terminal and nonterminal) symbols and size N (measured as the sum of the lengths of the right hands of the rules), a basic grammarbased representation of T takes N lg n bits of space. Our representation requires 2N lg n + N lg u + ɛ n lg n + o(N lg n) bits of space, for any 0 < ɛ ≤ 1. It can find the positions of the occ occurrences of a pattern of length m in T in O (m 2 /ɛ) lg lg u lg n + (m + occ) lg n time, and extract any substring of length ℓ of T in time O(ℓ + h lg(N/h)), where h is the height of the grammar tree.
LRMTrees: Compressed Indices, Adaptive Sorting, and Compressed Permutations ⋆
"... Abstract. LRMTrees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to index integer arrays in order to support range minim ..."
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Cited by 3 (1 self)
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Abstract. LRMTrees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to index integer arrays in order to support range minimum queries on them. We describe how they yield many other convenient results in a variety of areas: compressed succinct indices for range minimum queries on partially sorted arrays; a new adaptive sorting algorithm; and a compressed succinct data structure for permutations supporting direct and inverse application in time inversely proportional to the permutation’s compressibility. 1
Faster Topk Document Retrieval in Optimal Space ⋆
"... Abstract. We consider the problem of retrieving the k documents from a collection of strings where a given pattern P appears most often. We show that, by representing the collection using a Compressed Suffix Array CSA, a data structure using the asymptotically optimal CSA+o(n) bits can answer quer ..."
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Cited by 2 (2 self)
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Abstract. We consider the problem of retrieving the k documents from a collection of strings where a given pattern P appears most often. We show that, by representing the collection using a Compressed Suffix Array CSA, a data structure using the asymptotically optimal CSA+o(n) bits can answer queries in the time needed by CSA to find the suffix array interval of the pattern plus O(k lg 2 k lg ɛ n) accesses to suffix array cells, for any constant ɛ> 0. This is lg n / lg k times faster than the only previous solution using optimal space, lg k times slower than the fastest structure that uses twice the space, and lg 2 k lg ɛ n times the lowerbound cost of obtaining k document identifiers from the CSA. To obtain the result we introduce a tool called the sampled document array, which can be of independent interest. 1
A LempelZiv Compressed Structure for Document Listing ⋆
"... Abstract. Document listing is the problem of preprocessing a set of sequences, called documents, so that later, given a short string called the pattern, we retrieve the documents where the pattern appears. While optimaltime and linearspace solutions exist, the current emphasis is in reducing the s ..."
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Cited by 1 (1 self)
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Abstract. Document listing is the problem of preprocessing a set of sequences, called documents, so that later, given a short string called the pattern, we retrieve the documents where the pattern appears. While optimaltime and linearspace solutions exist, the current emphasis is in reducing the space requirements. Current document listing solutions build on compressed suffix arrays. This paper is the first attempt to solve the problem using a LempelZiv compressed index of the text collections. We show that the resulting solution is very fast to output most of the resulting documents, taking more time for the final ones. This makes this index particularly useful for interactive scenarios or when listing some documents is sufficient. Yet, it also offers a competitive space/time tradeoff when returning the full answers. 1