Efficient group based Hilbert encoding and decoding algorithms

Promoting Hilbert curve encoding and decoding efficiency is crucial for many Hilbert curve based applications. The current state-view based algorithms usually design 1-order state-views (1-SVs) and iteratively access these state-views in order-wise manner, leading to excessive state-view accesses. T...

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Published in:	Pattern recognition Vol. 167; p. 111718
Main Authors:	Jia, Lianyin, Wang, Songyu, Sun, Shaowen, Ding, Jiaman, Li, Mengjuan, You, Jinguo, Qiao, Shaojie
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.11.2025
Subjects:	Grouping Hilbert curve K-order state-views Virtual filling Hilbert curve Grouping Virtual filling K-order state-views
ISSN:	0031-3203
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Abstract	Promoting Hilbert curve encoding and decoding efficiency is crucial for many Hilbert curve based applications. The current state-view based algorithms usually design 1-order state-views (1-SVs) and iteratively access these state-views in order-wise manner, leading to excessive state-view accesses. To solve this problem, this paper uses a new paradigm and designs novel k-order state-views (k-SVs), which coalesces k state-view accesses into one access, significantly decreasing the state-view accesses. An efficient grouping framework is then designed to divide each input data into groups. Efficient virtual filling mechanisms are further developed to facilitate the k-SVs to all the groups, thus improving the time and space efficiency. Based on these techniques, efficient grouping encoding and decoding algorithms and the corresponding batched algorithms are designed. Compared with the existing ones, our algorithms reduce the time complexity from O(n) to O(n/k), where n is the total number of orders in each coordinate or a Hilbert code. Experimental results show that our algorithms run up to 3.18 times faster than the fastest competitor. •Novel k-order state-views merge k accesses into one, decreasing state-view accesses.•Virtual filling extends k-order views to all groups, boosting time/space efficiency.•Efficient algorithms achieve 3.18× speedup over competitors.
AbstractList	Promoting Hilbert curve encoding and decoding efficiency is crucial for many Hilbert curve based applications. The current state-view based algorithms usually design 1-order state-views (1-SVs) and iteratively access these state-views in order-wise manner, leading to excessive state-view accesses. To solve this problem, this paper uses a new paradigm and designs novel k-order state-views (k-SVs), which coalesces k state-view accesses into one access, significantly decreasing the state-view accesses. An efficient grouping framework is then designed to divide each input data into groups. Efficient virtual filling mechanisms are further developed to facilitate the k-SVs to all the groups, thus improving the time and space efficiency. Based on these techniques, efficient grouping encoding and decoding algorithms and the corresponding batched algorithms are designed. Compared with the existing ones, our algorithms reduce the time complexity from O(n) to O(n/k), where n is the total number of orders in each coordinate or a Hilbert code. Experimental results show that our algorithms run up to 3.18 times faster than the fastest competitor. •Novel k-order state-views merge k accesses into one, decreasing state-view accesses.•Virtual filling extends k-order views to all groups, boosting time/space efficiency.•Efficient algorithms achieve 3.18× speedup over competitors.
ArticleNumber	111718
Author	Sun, Shaowen Li, Mengjuan Ding, Jiaman Wang, Songyu You, Jinguo Jia, Lianyin Qiao, Shaojie
Author_xml	– sequence: 1 givenname: Lianyin surname: Jia fullname: Jia, Lianyin email: lianyinjia@kust.edu.cn organization: Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming, 650500, Yunnan, China – sequence: 2 givenname: Songyu surname: Wang fullname: Wang, Songyu email: wsongyu913@163.com organization: Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming, 650500, Yunnan, China – sequence: 3 givenname: Shaowen surname: Sun fullname: Sun, Shaowen email: qq1023401301@163.com organization: Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming, 650500, Yunnan, China – sequence: 4 givenname: Jiaman orcidid: 0000-0002-4419-1297 surname: Ding fullname: Ding, Jiaman email: jiamanding@kust.edu.cn organization: Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming, 650500, Yunnan, China – sequence: 5 givenname: Mengjuan surname: Li fullname: Li, Mengjuan email: lmjlykm@163.com organization: Library, Yunnan Normal University, Kunming, 650500, Yunnan, China – sequence: 6 givenname: Jinguo surname: You fullname: You, Jinguo email: jgyou@kust.edu.cn organization: Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming, 650500, Yunnan, China – sequence: 7 givenname: Shaojie surname: Qiao fullname: Qiao, Shaojie email: sjqiao@cuit.edu.cn organization: School of Software Engineering, Chengdu University of Information Technology, Chengdu, 610225, Sichuan, China
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Snippet	Promoting Hilbert curve encoding and decoding efficiency is crucial for many Hilbert curve based applications. The current state-view based algorithms usually...
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SubjectTerms	Grouping Hilbert curve K-order state-views Virtual filling
Title	Efficient group based Hilbert encoding and decoding algorithms
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