Unnikrishnan, A and Venkatesh, YV and Shankar, P (1987) Distribution of black nodes at various levels in a linear quadtree. In: Pattern Recognition Letters, 6 (5). pp. 341-342.
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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 2n × 2n 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:||Journal Article|
|Additional Information:||Copyright of this article belongs to Elsevier Science.|
|Date Deposited:||30 May 2009 18:50|
|Last Modified:||22 Oct 2010 10:03|
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