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Deletion in two-dimensional quad trees

By Hanan Samet

Communications of the ACM, Vol. 23 No. 12, Pages 703-710

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An algorithm for deletion in two-dimensional quad trees that handles the problem in a manner analogous to deletion in binary search trees is presented. The algorithm is compared with a proposed method for deletion which reinserts all of the nodes in the subtrees of the deleted node. The objective of the new algorithm is to reduce the number of nodes that need to be reinserted. Analysis for complete quad trees shows that the number of nodes requiring reinsertion is reduced to as low as 2/9 of that required by the old algorithm. Simulation tests verify this result. Reduction of the number of insertions has a similar effect on the number of comparison operations. In addition, the total path length (and balance) of the resulting tree is observed to remain constant or increase slightly when the new algorithm for deletion is used, whereas use of the old algorithm results in a significant increase in the total path length for large trees.

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