## Abstract

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 N-dimensional space so that every cell is visited at least once. Thus, a space-filling curve imposes a linear order of the cells in the N-dimensional space. 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 a brief knowledge of the mapping scheme provided by each space-filling curve. Irregularity is proposed as a quantitative measure of the quality of the mapping of the space-filling curve. Closed formulas are developed to compute the irregularity for any general dimension D with N points in each dimension for different space-filling curves. A comparative study of different space-filling curves with respect to irregularity is conducted and results are presented and discussed. The applicability of this research in the area of multimedia databases is illustrated with a discussion of the problems that arise.

Original language | English (US) |
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Title of host publication | International Conference on Information and Knowledge Management, Proceedings |

Editors | H. Paques, L. Liu |

Pages | 512-519 |

Number of pages | 8 |

State | Published - Dec 1 2001 |

Event | Proceedings of the 2001 ACM CIKM: 10th International Conference on Information and Knowledge Management - Atlanta, GA, United States Duration: Nov 5 2001 → Nov 10 2001 |

### Other

Other | Proceedings of the 2001 ACM CIKM: 10th International Conference on Information and Knowledge Management |
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Country/Territory | United States |

City | Atlanta, GA |

Period | 11/5/01 → 11/10/01 |