2-D Hilbert encoding and decoding algorithms on skewed data

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.