R-Trees: Theory and Applications

Manolopoulos, Yannis; Νανόπουλος, Αλέξανδρος; Papadopoulos, Apostolos N.; Theodoridis, Yannis

doi:10.1007/978-1-84628-293-5

Cited by 185 publications

(144 citation statements)

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“…The B-tree and its descendants are described in several basic textbooks on algorithms; a general structure called GiST (Generalized Search Tree, available from http://gist.cs.berkeley.edu) implements disk-based B-treestyle balancing for use in index structures in general, and has been used in several published implementations (including the original M-tree). For more information on recent developments in the R-tree family, see the book by Manolopoulos et al [107]. 34.…”

Section: B An Overview Of the Indexing Methodsmentioning

confidence: 99%

The Basic Principles of Metric Indexing

Hetland

2009

Studies in Computational Intelligence

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Summary. This chapter describes several methods of similarity search, based on metric indexing, in terms of their common, underlying principles. Several approaches to creating lower bounds using the metric axioms are discussed, such as pivoting and compact partitioning with metric ball regions and generalized hyperplanes. Finally, pointers are given for further exploration of the subject, including non-metric, approximate, and parallel methods.

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Section: B An Overview Of the Indexing Methodsmentioning

confidence: 99%

The Basic Principles of Metric Indexing

Hetland

2009

Studies in Computational Intelligence

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“…The root, inner branches contain information regarding the MBR or rectangle in case of leaf branches. An Rtree of order (n,M), has the following characteristics (Guttman 1984;Nanopoulos et al (2006)):…”

Section: Formulation Of the Rmap Frameworkmentioning

confidence: 99%

RMAP: a rectangular cuboid approximation framework for 3D environment mapping

et al. 2014

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This paper presents a rectangular cuboid approximation framework (RMAP) for 3D mapping. The goal of RMAP is to provide computational and memory efficient environment representations for 3D robotic mapping using axis aligned rectangular cuboids (RC). This paper focuses on two aspects of the RMAP framework: (i) An occupancy grid approach and (ii) A RC approximation of 3D environments based on point cloud density. The RMAP occupancy grid is based on the Rtree data structure which is composed of a hierarchy of RC. The proposed approach is capable of generating probabilistic 3D representations with multiresolution capabilities. It reduces the memory complexity in large scale 3D occupancy grids by avoiding explicit modelling of free space. In contrast to point cloud and fixed resolution cell representations based on beam end point observations, an approximation approach using point cloud density is presented. The proposed approach generates variable sized RC approximations that are memory efficient for axis aligned surfaces. Evaluation of the RMAP occupancy grid and approximation approach based on computational and memory complexity on different datasets shows the effectiveness of this framework for 3D mapping.

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“…This study prompted a wave of research papers and one can say that it gave birth to the new area of research. This research related to development of the new R-Tree variants [1,8,9], niche approaches [6,9], split techniques [10][11][12], concurrency techniques [13,14] etc. The study [6] states that there are several dozens of R-Tree variants.…”

Section: Fig 1: R-tree Examplementioning

confidence: 99%

“…According to [6] R-tree is a tree data structure, defined by a pair (m, M) with the following properties:  Each leaf node (unless it is the root) can host up to M entries, whereas the minimum allowed number of entries is m ≤ M/2. Each entry is of the form (mbr, oid), such that mbr is the MBR that spatially contains the object and oid is the object identifier.…”

mentioning

confidence: 99%