Planar stage graphs: Characterizations and applications

Bauernöppel, Frank; Kranakis, Evangelos; Kriz̧anc, Danny; Maheshwari, Anil; Sack, Jörg-Rüdiger; Urrutia, Jorge

doi:10.1016/s0304-3975(96)00201-0

Cited by 4 publications

(2 citation statements)

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“…Our range search structure is an improvement upon that of Mäkinen and Navarro [15], and we use it to improve previous results on designing space-efficient text indexes for substring search [7] and position-restricted substring search [15]. We also apply our structure to extend the previous result on representing a sequence of small integers succinctly [10], as well as a restricted version of orthogonal range search in which the query range is defined by two points in the point set [4]. More precisely, we present the following results, among which the first one is our main result and the rest are its applications:…”

Section: Our Resultsmentioning

confidence: 99%

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Succinct Orthogonal Range Search Structures on a Grid with Applications to Text Indexing

Bose

Maheshwari

et al. 2009

Lecture Notes in Computer Science

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Abstract. We present a succinct representation of a set of n points on an n × n grid using n lg n + o(n lg n) bits 3 to support orthogonal range counting in O(lg n/ lg lg n) time, and range reporting in O(k lg n/ lg lg n) time, where k is the size of the output. This achieves an improvement on query time by a factor of lg lg n upon the previous result of Mäkinen and Navarro [15], while using essentially the information-theoretic minimum space. Our data structure not only can be used as a key component in solutions to the general orthogonal range search problem to save storage cost, but also has applications in text indexing. In particular, we apply it to improve two previous space-efficient text indexes that support substring search [7] and position-restricted substring search [15]. We also use it to extend previous results on succinct representations of sequences of small integers, and to design succinct data structures supporting certain types of orthogonal range query in the plane.

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Section: Our Resultsmentioning

confidence: 99%

“…Thus: A restricted version of orthogonal range search. We consider a restricted version of range search (a weaker operation was proposed by Bauernöppel et al [4]) and we have the following theorem (see Appendix B for the proof):…”

Section: Applicationsmentioning

confidence: 99%