Orthogonal Range Searching for Text Indexing

Let D be a collection of string documents of n characters in total. The top-k document retrieval problem is to preprocess D into a data structure that, given a query (P, k), can return the k documents of D most relevant to pattern P. The relevance of a document d for a pattern P is given by a predefined ranking function w(P, d). Linear space and optimal query time solutions already exist for this problem. In this paper we consider a novel problem, document selection queries, which aim to report the kth document most relevant to P (instead of reporting all top-k documents). We present a data structure using O(n log n) space, for any constant > 0, answering selection queries in time O(log k/ log log n), and a linear-space data structure answering queries in time O(log k), given the locus node of P in a (generalized) suffix tree of D. We also prove that it is unlikely that a succinct-space solution for this problem exists with poly-logarithmic query time.

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“…y] can be reported efficiently. Many indexes offering different space and query time trade-offs exist [9,8].…”

Section: Hardness Of An Efficient Succinct Solutionmentioning

confidence: 99%

Ranked document selection

Munro¹,

Navarro

Shah

et al. 2020

Theoretical Computer Science

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“…Set x(l) = l and y(l) equal to the rank of suffix T [l...] in the lexicographical sort of the suffixes. To compute j ′ k ∈ I left = [a, (a+ b)/2] that has the maximal LCE value with a sampled position i = b−kτ ∈ I right = ((a+b)/2, b] we require two 3-sided range successor queries, see detailed definitions in [17]. The first is a range [a, (a + b)/2] × (−∞, y(i) − 1] which returns the point within the range with y-coordinate closest to, and less-than, y(i).…”

Section: Preprocessingmentioning

confidence: 99%

Longest Common Extensions in Sublinear Space

Bille

Gørtz

Knudsen

et al. 2015

Combinatorial Pattern Matching

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The longest common extension problem (LCE problem) is to construct a data structure for an input string T of length n that supports LCE(i, j) queries. Such a query returns the length of the longest common prefix of the suffixes starting at positions i and j in T . This classic problem has a well-known solution that uses O(n) space and O(1) query time. In this paper we show that for any trade-off parameter 1 ≤ τ ≤ n, the problem can be solved in O( n τ ) space and O(τ ) query time. This significantly improves the previously best known time-space trade-offs, and almost matches the best known time-space product lower bound.

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“…Such a query can be answered optimally in O (log log n + occ) time using an O (n log n)-word space structure, where > 0 is any arbitrary small constant [1]. See [20,10] for connections between text indexing and range searching.…”

Section: Two-dimensional Orthogonal Range Reportingmentioning

confidence: 99%

“…Work supported by NSERC of Canada and the Canada Research Chairs program. are two of the natural extensions of this problem, and have been studied extensively [2,11,15,8,18,30,31,14,6,19,20]. These problems have several applications in information retrieval, bioinformatics, data mining, and internet traffic analysis [7,13].…”

Section: Introduction and Related Workmentioning

confidence: 99%

Less space: Indexing for queries with wildcards

Lewenstein

Munro

Raman

et al. 2014

Theoretical Computer Science

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Text indexing is a fundamental problem in computer science, where the task is to index a given text (string) T [1..n], such that whenever a pattern P [1..p] comes as a query, we can efficiently report all those locations where P occurs as a substring of T . In this paper, we consider the case when P contains wildcard characters (which can match with any other character). The first non-trivial solution for the problem was given by Cole et al.[11], where the index space is O (n log k n) words or O (n log k+1 n) bits and the query time is O (p +2 h log log n +occ), where k is the maximum number of wildcard characters allowed in P , h ≤ k is the number of wildcard characters in P and occ represents the number of occurrences of P in T . Even though many indexes offering different space-time trade-offs were later proposed, a clear improvement on this result is still not known. In this paper, we first propose an O (n log k+ n) bits index achieving the same query time as the of Cole et al.'s index, where 0 < < 1 is an arbitrary small constant. Then we propose another index of size O (n log k n log σ ) bits, but with a slightly higher query time of O (p + 2 h log n + occ), where σ denotes the alphabet set size.We also study a related problem, where the task is to index a collection of documents (of n characters in total) so as to find the number of distinct documents containing a query pattern P . For the case where P contains at most a single wildcard character, we propose an O (n log n)-word index with optimal O (p) query time.Published by Elsevier B.V.

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Orthogonal Range Searching for Text Indexing

Cited by 24 publications

References 104 publications

Ranked document selection

Ranked document selection

Longest Common Extensions in Sublinear Space

Less space: Indexing for queries with wildcards

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