New upper bounds for generalized intersection searching problems

Bozanis, Panayiotis; Kitsios, Nectarios; Makris, Christos; Tsakalidis, Athanasios K.

doi:10.1007/3-540-60084-1_97

Cited by 27 publications

(26 citation statements)

References 11 publications

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“…The wavelet tree for C takes O(n log n) bits and does this counting in time proportional to its height, O(log n). This already matches the best known solution, due to Bozanis, Kitsios, Makris and Tsakalidis [6]. In the rest of this section we show how to reduce the space bound to n log σ + O(n log log n) bits.…”

Section: Countingsupporting

confidence: 73%

“…This information could be, for example, the minimum or maximum value in S[i, j] [12], the element with a specified rank in sorted order [15] (e.g., the median [7]), the mode [17], a complete list of the distinct elements [31], the frequencies of the elements [35], a list of the k most frequent elements for a given k [20], or the number of distinct elements [6]. In this paper, motivated by problems in document retrieval, we consider the latter three kinds of problems, which are often referred to as "colored" range queries: colored range listing (with or without color frequencies), colored range top-k queries, and colored range counting.…”

Section: Introductionmentioning

confidence: 99%

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Colored Range Queries and Document Retrieval

Gagie

Navarro

Puglisi

2010

String Processing and Information Retrieval

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Abstract. Colored range queries are a well-studied 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 one-dimensional colored range queries -colored range listing, colored range top-k 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 high-order entropies of the library of documents. We then show how (approximate) colored top-k queries can be reduced to (approximate) range-mode 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.

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Section: Countingsupporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Colored Range Queries and Document Retrieval

Gagie

Navarro

Puglisi

2010

String Processing and Information Retrieval

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“…For counting, we use the solution described in [7]. The data structure requires O(n) space and a color counting query takes O(log n) time.…”

Section: Document Counting and Reportingmentioning

confidence: 99%

Cross-Document Pattern Matching

Kucherov

Nekrich

Starikovskaya

2012

Combinatorial Pattern Matching

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Abstract. We study a new variant of the string matching problem called cross-document string matching, which is the problem of indexing a collection of documents to support an efficient search for a pattern in a selected document, where the pattern itself is a substring of another document. Several variants of this problem are considered, and efficient linear-space solutions are proposed with query time bounds that either do not depend at all on the pattern size or depend on it in a very limited way (doubly logarithmic). As a side result, we propose an improved solution to the weighted level ancestor problem.

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“…Solutions for standard problems yield outputinsensitive solutions for their generalized chromatic counterparts. For this reason they attracted a lot of research [2,9,10,17,18,14,23,24]. These papers present a number of efficient, mainly theoretical, algorithms that are tailored to the main-memory context.…”

Section: Related Workmentioning

confidence: 99%

“…This type of query is denoted as Categorical Range Query (CRQ) 1 and the attribute that the grouping is based upon is called categorical attribute. CRQs have been comprehensively studied in the research fields of computational geometry and main-memory data structures [2,9,10,11,17,18,20,23]. In contrast, much less attention has been given to supporting CRQs in large databases.…”

Section: Introductionmentioning

confidence: 99%

Categorical Range Queries in Large Databases

Νανόπουλος

Bozanis

2003

Advances in Spatial and Temporal Databases

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Abstract. In this paper, we introduce the categorical (a.k.a. chromatic) range queries (CRQs) in the context of large, disk-resident data sets, motivated by the fact that CRQs are conceptually simple and emerge often in DBMSs. On the basis of spatial data structures, and R-trees in particular, we propose a multi-tree index that follows the broad concept of augmenting nodes with additional information to accelerate queries. Augmentation is examined with respect to maximal/minimal points in subtrees, the properties of which are exploited by the proposed searching algorithm to effectively prune the search space. Detailed experimental results, with both real and synthetic data, illustrate the significant performance gains (up to an order of magnitude) due to the proposed method, compared to the regular range query (followed by the filtering w.r.t. categories) and to a naive R-tree augmentation method.

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New upper bounds for generalized intersection searching problems

Cited by 27 publications

References 11 publications

Colored Range Queries and Document Retrieval

Colored Range Queries and Document Retrieval

Cross-Document Pattern Matching

Categorical Range Queries in Large Databases

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