A data structure for orthogonal range queries

Lueker, George S.

doi:10.1109/sfcs.1978.1

Cited by 154 publications

(84 citation statements)

References 9 publications

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“…It allows to report all points in a given range efficiently, and can be used in two or higher dimensions. Range tree was separately introduced by different people [3,18,22,29]. In this paper, we first use 2D range trees while working on trapezoid graphs and use k-dimensional range trees later to apply for k-trapezoid graphs.…”

Section: Range Treementioning

confidence: 99%

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Efficient maximum matching algorithms for trapezoid graphs

Le²,

2017

ejgta

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Trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. Many NPhard problems can be solved in polynomial time if they are restricted on trapezoid graphs. A matching in a graph is a set of pairwise disjoint edges, and a maximum matching is a matching of maximum size. In this paper, we first propose an O(n(log n)3 ) algorithm for finding a maximum matching in trapezoid graphs, then improve the complexity to O(n(log n)2 ). Finally, we generalize this algorithm to a larger graph class, namely k-trapezoid graphs. To the best of our knowledge, these are the first efficient maximum matching algorithms for trapezoid graphs.

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Section: Range Treementioning

confidence: 99%

“…Recall that a range tree can be constructed by using the fractional cascading technique [22,28] as follows. First, sort the points with respect to the increasing x-coordinate, and build a binary search tree over them.…”

Section: S-range Treementioning

confidence: 99%

Efficient maximum matching algorithms for trapezoid graphs

Le²,

2017

ejgta

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“…For a point u being considered, L(u) and R(u) can be found in O(log n) time using range tree with fractional cascading [19]. Building the range tree takes O(n log n) time and O(n log n) extra space.…”

Section: Algorithm 1 An Algorithm To Hit Induced Skyline Rectanglesmentioning

confidence: 99%

Hitting and Piercing Rectangles Induced by a Point Set

Rajgopal

Ashok

Govindarajan

et al. 2013

Lecture Notes in Computer Science

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Abstract. We consider various hitting and piercing problems for the family of axis-parallel rectangles induced by a point set. Selection Lemmas on induced objects are classical results in discrete geometry that have been well studied and have applications in many geometric problems like weak epsilon nets and slimming Delaunay triangulations. Selection Lemma type results typically bound the maximum number of induced objects that are hit/pierced by a single point. First, we prove an exact result on the strong and the weak variant of the First Selection Lemma for rectangles. We also show bounds for the Second Selection Lemma which improve upon previous bounds when there are near-quadratic number of induced rectangles. Next, we consider the hitting set problem for induced rectangles. This is a special case of the geometric hitting set problem which has been extensively studied. We give efficient algorithms and show exact combinatorial bounds on the hitting set problem for two special classes of induced axis-parallel rectangles. Finally, we show that the minimum hitting set problem for all induced lines is NP-Complete.

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“…SpiDeR uses a range tree [Lue78] data structure to identify spikes in a time range. The range trees allows SpiDeR to aggregate spikes that are deemed to be suspicious in up to one week.…”

Section: Spidermentioning

confidence: 99%

Mixed Spatial and Nonspatial Problems in Location Based Services

Ballesteros¹

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All rights reserved.iii DEDICATION Esta Disertacion va dedicada muy especialmente a mi familia. Primero mis padres, Elssy y Jaime, que me dieron todas las herramientas necesarias para poder cumplir mis metas. El amor, el sacrificio y dedicacion con que nos formaron a mis hermanos y a mi seran siempre motivo de inspiracion para continuar adelante. A mis hermanos Lili, Meli, Randy e Isabella, por apoyarme y darme muchas alegrias y motivos de orgullo.Por supuesto, no podria faltar la dedicacion a mi hermosa esposa, Pily. Desde que comenzamos juntos este viaje, siempre ha estado conmigo compartiendo todos los momentos, lo mas felices y los mas dificiles y nunca ha desistido. Para ella, que es mi fuerza inspiradora y mi amor, va dedicada esta disertacion. Finalmente, quisiera dedicar este logro a mi Maestro. El sin duda me ha dado todo lo que tengo y esto es simplemente parte de su obra. Gracias por todo. Special thanks goes to Dr. Bogdan Carbunar, who has been a great collaborator and teacher, and to Mr. Mahmudur Rahman. We all created such an exceptional team and we were able to contribute in several aspects in our research. Their valuable insights and feedback were the key to publish our work. problem. To address this, we introduce SpsJoin, a framework for computing spatial set-similarity joins. SpsJoin handles combined similarity queries that involve textual and spatial constraints simultaneously. LBSs use this system to tackle different types of problems, such as deduplication, geolocation enhancement and record linkage. We define the spatial set-similarity join problem in a general case and propose an algorithm for its efficient computation. Our solution utilizes parallel computing with MapReduce to handle scalability issues in large geospatial databases.Second, applications that use geolocation data are seldom concerned with ensuring the privacy of participating users. To motivate participation and address privacy concerns, we propose iSafe, a privacy preserving algorithm for computing safety snapshots of co-located mobile devices as well as geosocial network users. vi iSafe combines geolocation data extracted from crime datasets and geosocial networks such as Yelp. In order to enhance iSafe's ability to compute safety recommendations, even when crime information is incomplete or sparse, we need to identify relationships between Yelp venues and crime indices at their locations. To achieve this, we use SpsJoin on two datasets (Yelp venues and geolocated businesses) to find venues that have not been reviewed and to further compute the crime indices of their locations. Our results show a statistically significant dependence between location crime indices and Yelp features.Third, review centered LBSs (e.g., Yelp) are increasingly becoming targets of malicious campaigns that aim to bias the public image of represented businesses.Although Yelp actively attempts to detect and filter fraudulent reviews, our experiments showed that Yelp is still vulnerable. Fraudulent LBS information also impacts the ability of iSafe t...

show abstract

A data structure for orthogonal range queries

Cited by 154 publications

References 9 publications

Efficient maximum matching algorithms for trapezoid graphs

Efficient maximum matching algorithms for trapezoid graphs

Hitting and Piercing Rectangles Induced by a Point Set

Mixed Spatial and Nonspatial Problems in Location Based Services

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