On Multi-dimensional Hilbert Indexings

Indexing schemes for grids based on space- lling curves (e.g., Hilbert indexings) nd applications in numerous elds. Hilbert curves yield the most simple and popular scheme. We extend the concept of curves with Hilbert property to arbitrary dimensions and present rst results concerning their structural analysis that also simplify their applicability. As we show, Hilbert indexings can be completely described and analyzed by \generating elements of order 1", thus, in comparison with previous work, reducing their structural complexity decisively.

• Type: Conference
• Year: 1998
• Where: COCOON
• Authors: Jochen Alber, Rolf Niedermeier
• Keywords: COCOON 1998, Combinatorics, Hilbert, Hilbert Indexings, Hilbert Property