On Multi-dimensional Hilbert Indexings
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
Path planning of mobile landmarks for localization in wireless sensor networks
Computer Communications
Alternative Algorithm for Hilbert's Space-Filling Curve
IEEE Transactions on Computers
Compact Hilbert indices: Space-filling curves for domains with unequal side lengths
Information Processing Letters
On-Line Signature Matching Based on Hilbert Scanning Patterns
ICB '09 Proceedings of the Third International Conference on Advances in Biometrics
A generalized 3-D Hilbert scan using look-up tables
Journal of Visual Communication and Image Representation
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The subject of this paper is a means of converging to a set of numbers in certain mathematical programming problems where a conventional programming method is not possible. The space filling curve is shown to provide a tool for doing this. An algorithm for generating such a curve is presented; the resulting space filling curve is a generalization of a mapping which Hilbert gave for the unit square only, in geometric form only. The following topics are discussed: convergence to solutions of systems of equalities or inequalities, convergence to minima, the advantages of the present space filling curve over other known space filling curves, some experimental results, and the relation between these methods and the standard methods of mathematical programming.