Unnikrishnan, A. ; Venkatesh, Y. V. ; Shankar, Priti
(1987)
*Distribution of black nodes at various levels in a linear quadtree*
Pattern Recognition Letters, 6
(5).
pp. 341-342.
ISSN 0167-8655

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Official URL: http://www.sciencedirect.com/science/article/pii/0...

Related URL: http://dx.doi.org/10.1016/0167-8655(87)90017-1

## Abstract

The distribution of black leaf nodes at each level of a linear quadtree is of significant interest in the context of estimation of time and space complexities of linear quadtree based algorithms. The maximum number of black nodes of a given level that can be fitted in a square grid of size 2^{n} × 2^{n} can readily be estimated from the ratio of areas. We show that the actual value of the maximum number of nodes of a level is much less than the maximum obtained from the ratio of the areas. This is due to the fact that the number of nodes possible at a level k, 0≤k≤n - 1, should consider the sum of areas occupied by the actual number of nodes present at levels k + 1, k + 2, ..., n - 1.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

Keywords: | Quadtree |

ID Code: | 57131 |

Deposited On: | 26 Aug 2011 02:34 |

Last Modified: | 26 Aug 2011 02:34 |

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