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. 2019 Mar 25;9:5059. doi: 10.1038/s41598-019-41451-3

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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An example to illustrate the construction of RTFC and the query using RTFC. (a) The original interval set and the corresponding indices. (b) The resulting tree structure and the query processes. The red arrow lines represent the search path of x₁ = 2.5 and x₂ = 9.5. The item bounded by a red box in a node represents the searched index in the data array for y₁ = 2.5. The green shaded intervals represent the result intervals. (c) Range query transformed from interval query.