Corner-based splitting: An improved node splitting algorithm for R-tree

Sleit, Azzam; Al-Nsour, Esam

doi:10.1177/0165551513516709

Cited by 14 publications

(6 citation statements)

References 10 publications

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“…The SOLD algorithm performance was tested against two algorithms: R-tree Quad algorithm [14] and the CBS algorithm [26]. Tests were performed on Intel Core i3-3120M, 2.5 GHz CPU, 4 GB memory, running Windows 10 Pro-32 bit.…”

Section: Experiments and Results Analysismentioning

confidence: 99%

“…Corner-based splitting (CBS) algorithm [26] starts by finding the overflown node’s MBR centre point ( CovRectX Cen , CovRectY Cen ) and the centre point of each object’s MBR ( ObjX Cen , ObjY Cen ). Using the centre points, the algorithm determines which corner of the overflown node’s MBR is closer to that object centre (four corners in case of two dimensions: C0( X l , Y l ), C1 ( X h , Y l ), C2 ( X h , Y h ) and C3 ( X l , Y h )).…”

Section: Related Workmentioning

confidence: 99%

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SOLD: A node-Splitting algorithm for R-tree based on Objects’ Locations Distribution

Al-Nsour

Sleit

Alshraideh

2018

Journal of Information Science

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Spatial data indexing methods are of extreme importance as they massively build up as a result of the explosive growth in capturing data with spatial features. No matter how much the data size is, eventually it will reside on disk pages. Disk pages have to be properly indexed to preserve spatial properties of objects, optimise disk space usage and improve objects’ retrieval performance. One of the most popular spatial data indexes is the R-tree which is a height balanced tree data structure, where leaf nodes resemble disk pages and contain pointers to objects’ locations. A single tree node can host up to a maximum number of objects, where any more insertion makes it an overflown node and it has to be split. Better splits lead to better index performance and more utilisation of disk space. In this work, we introduce a new way of finding the most proper split for an overflown node in the R-tree index. The proposed work scans – in a linear cost – the overflown node’s objects once to identify the distribution of objects’ locations (minimum bounding rectangles (MBRs)) in relative to its node’s bounding rectangle (node’s MBR). It uses objects’ locations to calculate – for each main axis – the split quality factors: expected overlap between resulting nodes, objects distribution evenness among resulting nodes and the perimeter of resulting nodes. The axis with better combined quality factors values is selected as the split axis. The Splitting based on Objects’ Locations Distribution (SOLD) algorithm was implemented and tested against two other splitting algorithms, experiments using synthetic and real data files showed good results and it outperformed both algorithms in index creation tests and data retrieval tests.

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Section: Experiments and Results Analysismentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

SOLD: A node-Splitting algorithm for R-tree based on Objects’ Locations Distribution

Al-Nsour

Sleit

Alshraideh

2018

Journal of Information Science

Self Cite

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“…This enhancement suggests that when distributing the entries between the output nodes, all ( M + 1) entries of an overflown node are sorted twice. Sleit and Al-Nsour [10] proposed a corner-based splitting (CBS) algorithm. The CBS algorithm improves the algorithm of Al-Badarneh et al [9], divides a node into four equal parts, dynamically selects the appropriate splitting axis according to the number of data of each partition and splits a saturated node into two nodes, thus avoiding the diagonal effect that exists in the algorithm.…”

Section: Related Workmentioning

confidence: 99%

LAZY R-tree: The R-tree with lazy splitting algorithm

Yang

Bai

et al. 2019

Journal of Information Science

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The spatial index is a data structure formed according to the position and shape of the spatial object or the relationship between the spatial objects according to certain rules, and the spatial data is managed by an effective spatial data structure. The quality of a spatial index directly affects the performance of spatial queries. The R-tree index structure is a highly efficient spatial index. According to the R-tree query rule, when performing spatial query, most data that is not related to the query condition can be filtered out, and finally, a few leaf nodes can be accessed to query the data satisfying the condition. Its query performance is affected by factors such as non-leaf node overlap and node space utilisation. This article proposes a lazy splitting method to improve the R-tree construction process. The scheme works as follows: (1) When a node overflows, it creates an overflow node for that node and all overflow nodes are saved in a hash table. (2) If the node continues to insert data, the data are added to its overflow node. (3) When an overflow node is saturated, the node and its overflow node are split into two saturated nodes. We use both simulated and actual data to perform experiments. The experimental results show that an R-tree constructed by the lazy algorithm is superior to an R-tree constructed using the original R-tree PM algorithm or the corner-based splitting (CBS) algorithm based on the number of splits created, the node space used and the efficiency of region queries and k-nearest neighbour (kNN) queries.

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“…Good node splitting strategy is fundamental; it affects the final shape of the index, the overlap area between nodes, and the overall performance of the index [12]. In the search for suitable splitting strategies, a vast amount of research was proposed in the literature.…”

Section: Introductionmentioning

confidence: 99%

“…In the search for suitable splitting strategies, a vast amount of research was proposed in the literature. In general, they were designed to; reduce overlap area between tree nodes [11], getting more even distribution of objects among nodes [12], and having more squared nodes shapes [13]. These strategies are referred to as the node splitting quality factors.…”

Section: Introductionmentioning

confidence: 99%

Evaluating Various Quality Factors for Splitting Nodes in Tree-Structured Spatial Indices

Al-Nsour¹,

Sleit²,

Alshraideh³

2018

IJCA

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The massive increase of multi-dimensional (spatial) data collected, either in size or veracity, has demanded better spatial index techniques able to handle efficient storing and fast retrieval of spatial objects. No matter how big the data are, eventually it will reside on physical storage media arranged as a series of logical blocks with prefixed sizes resembling nodes in tree-structured spatial indices. Good node splitting strategy is essential since it affects; the final shape of the index, the overlap area between nodes, and the overall index performance. Better node splitting process results will be obtained if multiple splitting strategies (quality factors) were combined to govern the split decision, and it will eliminate the need for dynamic or static tree packing. Three widely used quality factors; minimizing total overlap area, even distribution of objects, and squared nodes' margins, along with a fourth factor named the "preferred-axis" were merged in one combined value to govern the split decision. Provided results, for the index creation tests and different sized window queries performance, indicate the superiority of the combined quality factors strategy in comparison of other unilateral usage of quality factors. Provided results showed that combined quality-factors strategy had outperformed different two strategies found in the literature in both index creation tests and index performance tests. The obtained results were achieved without the need for any dynamic or static tree packing.

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Corner-based splitting: An improved node splitting algorithm for R-tree

Cited by 14 publications

References 10 publications

SOLD: A node-Splitting algorithm for R-tree based on Objects’ Locations Distribution

SOLD: A node-Splitting algorithm for R-tree based on Objects’ Locations Distribution

LAZY R-tree: The R-tree with lazy splitting algorithm

Evaluating Various Quality Factors for Splitting Nodes in Tree-Structured Spatial Indices

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