Gray Codes for Partial Match and Range Queries
IEEE Transactions on Software Engineering
Fractals for secondary key retrieval
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Digital halftoning with space filling curves
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Space-filling curves and their use in the design of geometric data structures
Theoretical Computer Science - Special issue: Latin American theoretical informatics
Irregularity in multi-dimensional space-filling curves with applications in multimedia databases
Proceedings of the tenth international conference on Information and knowledge management
A class of data structures for associative searching
PODS '84 Proceedings of the 3rd ACM SIGACT-SIGMOD symposium on Principles of database systems
Analysis of the Clustering Properties of the Hilbert Space-Filling Curve
IEEE Transactions on Knowledge and Data Engineering
DOT: A Spatial Access Method Using Fractals
Proceedings of the Seventh International Conference on Data Engineering
High Dimensional Similarity Search With Space Filling Curves
Proceedings of the 17th International Conference on Data Engineering
Hilbert R-tree: An Improved R-tree using Fractals
VLDB '94 Proceedings of the 20th International Conference on Very Large Data Bases
Scalable QoS-Aware Disk-Scheduling
IDEAS '02 Proceedings of the 2002 International Symposium on Database Engineering & Applications
XZ-Ordering: A Space-Filling Curve for Objects with Spatial Extension
SSD '99 Proceedings of the 6th International Symposium on Advances in Spatial Databases
Automatically and accurately conflating orthoimagery and street maps
Proceedings of the 12th annual ACM international workshop on Geographic information systems
IEEE Transactions on Knowledge and Data Engineering
Neighbor-finding based on space-filling curves
Information Systems
Mapping with Space Filling Surfaces
IEEE Transactions on Parallel and Distributed Systems
An N-Dimensional Pseudo-Hilbert Scan for Arbitrarily-Sized Hypercuboids
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online data visualization of multidimensional databases using the hilbert space-filling curve
VIEW'06 Proceedings of the 1st first visual information expert conference on Pixelization paradigm
Journal of Visual Languages and Computing
Irregularity in high-dimensional space-filling curves
Distributed and Parallel Databases
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A space-filling curve is a way of mapping the multi-dimensional space into the one-dimensional space. It acts like a thread that passes through every cell element (or pixel) in the D-dimensional space so that every cell is visited exactly once. There are numerous kinds of space-filling curves. The difference between such curves is in their way of mapping to the one dimensional space. Selecting the appropriate curve for any application requires knowledge of the mapping scheme provided by each space-filling curve. A space-filling curve consists of a set of segments. Each segment connects two consecutive multi-dimensional points. Five different types of segments are distinguished, namely, Jump, Contiguity, Reverse, Forward, and Still. A description vector V=(J,C,R,F,S), where J,C,R,F, and S, are the percentages of Jump, Contiguity, Reverse, Forward, and Still segments in the space-filling curve, encapsulates all the properties of a space-filling curve. The knowledge of V facilitates the process of selecting the appropriate space-filling curve for different applications. Closed formulas are developed to compute the description vector V for any D-dimensional space and grid size N for different space-filling curves. A comparative study of different space filling curves with respect to the description vector is conducted and results are presented and discussed.