Efficient computation of the convex hull on sets of points stored in a k-tree compact data structure

Castro, Juan Felipe; Romero, Miguel; Gutiérrez, Gilberto; Caniupan, Monica; Quijada-Fuentes, Carlos

doi:10.1007/s10115-020-01486-9

Cited by 5 publications

(1 citation statement)

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“…This process continues until reaching cells of size 1 × 1. The versatility of this compact structure extends across diverse application domains, including graph representations [7], raster data [21], and points in N 2 [14]. Noteworthy is the k 2 -tree's ability to store static sets of points without relying on pointers, making it a foundational structure for comparative analysis in our study.…”

Section: Related Workmentioning

confidence: 99%

cKd-tree: A Compact Kd-tree

Gutiérrez,

Torres-Avilés,

Caniupán

2024

IEEE Access

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In the context of Big Data scenarios, the presence of extensive static datasets is not uncommon. To facilitate efficient queries on such datasets, the utilization of multiple indexes, such as the Kd-tree, becomes imperative. The current scale of managed points may, however, exceed the capacity of primary memory, posing a significant challenge. In this article we introduce cKd-tree, a compact data structure designed to represent a Kd-tree efficiently. The structure cKd-tree is essentially an encoding of the spiral code sequence of points within an implicit Kd-tree (iKd-tree) using Directly Addressable Codes (DACs). The unique feature of cKd-tree lies in its ability to perform spiral encoding and decoding of points by relying solely on knowledge of their parent points within the iKd-tree. This inherent property, combined with DACs' direct access capability to sequence elements, enables cKd-tree to traverse and explore the tree while decoding only the nodes relevant to queries. The article details the algorithms necessary for creating and manipulating a cKd-tree, as well as algorithms for evaluating two fundamental queries over points: the point query and the range query. To assess the performance of cKd-tree, a series of experiments are conducted, comparing it with iKd-tree and k 2 -tree data structures. The evaluation metrics include compression efficiency and execution time of queries. cKd-tree achieves a compression ratio comparable to that of k 2 -tree, approximately 70%, demonstrating heightened efficiency, particularly in scenarios characterized by sparse data. Additionally, consistent with expectations, k 2 -tree exhibits superior performance in querying individual points, whereas cKd-tree outperforms in the context of aggregate data queries, such as range queries.INDEX TERMS Compression, indices, spatial data, spatial points, spatial queries.

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Section: Related Workmentioning

confidence: 99%