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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
ISSN:0031-3203
DOI:10.1016/j.patcog.2025.111718