关键词: 降维 Hilbert 分划 算法

Abstract:

The Hilbert curve is an important means in high-dimensional structural reduction, which is widely used in multi-dimensional index and image processing  . The traditional coding algorithm is usually based on replicating part of the Hilbert curve, and using some operations like rotation to compose the total configuration, and it has a complexity of O（n^2 ）. After investigating the essential characteristics of the Hilbert curve, this paper puts forward  a new Hilbert coding algorithm with a complexity of O（nlogn） based on partitioning, and analyses the algorithm with practical instances.

Key words: （dimensional reduction, Hilbert, partitioning, algorithm）