Z-order curve, as an efficient method for reducing spatial dimensionality, has found widespread applications in various fields. Although existing state-of-the-art algorithms design dimensional lookup tables, they suffer from the drawback of high table lookup frequency. To address this issue, we propose a novel and efficient g-order Value LookUp Table (namely VLUT_g), which can directly obtain the corresponding code (or coordinate) through coordinate (or code). Building upon this, we present efficient Z-order curve encoding and decoding algorithms based on VLUT_g, and further design the coarse-grained and fine-grained parallel Z-order curve encoding and decoding algorithms based on Graphics Processing Units (GPU), thus significantly enhancing the efficiency of Z-order curve encoding and decoding. We further propose VLUT_g combining with B⁺-tree (VLUT_g-B⁺) algorithm to extend our algorithms to support spatial range query. Experimental results on multiple datasets demonstrate that our encoding and decoding algorithms perform well when g is set to 8, with encoding 25 million 32-order discrete coordinate data requiring only 6.556 ms, achieving an efficiency improvement of two orders of magnitude compared to the fastest known algorithm. Besides, VLUT_g-B⁺ can be up to 5.67× faster than R*-tree on spatial range query.

Hilbert encoding and decoding are fundamental steps in many Hilbert curve based applications. However, existing algorithms are not very efficient when the data distribution is skewed. This paper shows that for a coordinate with the specific first m orders, the code of the first m orders is a multiple of its corresponding first order code. For a code with the specific first m orders, the coordinate of the first m orders is a multiple of its corresponding first order coordinate. These findings were used to develop an algorithm that skips the first m orders of the Hilbert encoding (SFO-HE) and another algorithm that skips the first m orders of the Hilbert decoding (SFO-HD). These algorithms exploit efficient bit operations and fast bit set detections to improve the encoding and decoding efficiencies for data skewed to the 4 corners of the Hilbert space. Extensive tests show that these two algorithms have good skewness adaptability and outperform existing algorithms on specific skewed data.