### 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 |
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Pages | 512-519 |

Number of pages | 8 |

Publication status | Published - 1 Dec 2001 |

Externally published | Yes |

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

### Other

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

City | Atlanta, GA |

Period | 5/11/01 → 10/11/01 |

### Fingerprint

### ASJC Scopus subject areas

- Decision Sciences(all)
- Business, Management and Accounting(all)

### Cite this

*Irregularity in multi-dimensional space-filling curves with applications in multimedia databases*. 512-519. Paper presented at Proceedings of the 2001 ACM CIKM: 10th International Conference on Information and Knowledge Management, Atlanta, GA, United States.

**Irregularity in multi-dimensional space-filling curves with applications in multimedia databases.** / Mokbel, Mohamed; Aref, Walid G.

Research output: Contribution to conference › Paper

}

TY - CONF

T1 - Irregularity in multi-dimensional space-filling curves with applications in multimedia databases

AU - Mokbel, Mohamed

AU - Aref, Walid G.

PY - 2001/12/1

Y1 - 2001/12/1

N2 - 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.

AB - 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.

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M3 - Paper

SP - 512

EP - 519

ER -