Encoding and Decoding Algorithms for Arbitrary Dimensional Hilbert Order

2016/01/06 by Hui Liu, Tao Cui, Liu, Hui +5
Computer Science · #FOS: Computer and information sciences #Symbolic Computation (cs.SC) #cs.SC

paper · pdf · doi:10.48550/arxiv.1601.01274

arxiv created 2016/01/06 · arxiv updated 2016/01/07

Abstract

Hilbert order is widely applied in many areas. However, most of the algorithms are confined to low dimensional cases. In this paper, algorithms for encoding and decoding arbitrary dimensional Hilbert order are presented. Eight algorithms are proposed. Four algorithms are based on arithmetic operations and the other four algorithms are based on bit operations. For the algorithms complexities, four of them are linear and the other four are constant for given inputs. In the end of the paper, algorithms for two dimensional Hilbert order are presented to demonstrate the usage of the algorithms introduced.

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