Multiattribute hashing using Gray codes
SIGMOD '86 Proceedings of the 1986 ACM SIGMOD international conference on Management of data
Gray Codes for Partial Match and Range Queries
IEEE Transactions on Software Engineering
Analysis of the Hilbert curve for representing two-dimensional space
Information Processing Letters
Space-filling curves and their use in the design of geometric data structures
Theoretical Computer Science - Special issue: Latin American theoretical informatics
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
Analyzing locality over a P2P computing architecture
Journal of Network and Computer Applications
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Space filling curves have for long been used in the design of data structures for multidimensional data. A fundamental quality metric of a space filling curve is its "clustering number" with respect to a class of queries, which is the average number of contiguous segments on the space filling curve that a query region can be partitioned into. We present a characterization of the clustering number of a general class of space filling curves, as well as the first non-trivial lower bounds on the clustering number for any space filling curve. Our results also answer an open problem that was posed by Jagadish in 1997.