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Hanan Samet

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Research and Advances Dec 1 1980

Deletion in two-dimensional quad trees

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.
Research and Advances Mar 1 1980

Region representation: boundary codes from quadtrees

There has been recent interest in the use of quadtrees to represent regions in an image. It thus becomes desirable to develop efficient methods of conversion between quadtrees and other types of region representations. This paper presents an algorithm for converting from quadtrees to a simple class of boundary codes. The algorithm is shown to have an execution time proportional to the perimeter of the region.
Research and Advances Jul 1 1978

Proving the correctness of heuristically optimized code

A system for proving that programs written in a high level language are correctly translated to a low level language is described. A primary use of the system is as a postoptimization step in code generation. The low level language programs need not be generated by a compiler and in fact could be hand coded. Examples of the usefulness of such a system are given. Some interesting results are the ability to handle programs that implement recursion by bypassing the start of the program, and the detection and pinpointing of a wide class of errors in the low level language programs. The examples demonstrate that optimization of the genre of this paper can result in substantially faster operation and the saving of memory in terms of program and stack sizes.
Artificial Intelligence and Machine Learning

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