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The trie data structure has many properties which make it especially attractive for representing large files of data. These properties include fast retrieval time, quick unsuccessful search determination, and finding the longest match to a given identifier. The main drawback is the space requirement. In this paper the concept of trie compaction is formalized. An exact algorithm for optimal trie compaction and three algorithms for approximate trie compaction are given, and an analysis of the three algorithms is done. The analyses indicate that for actual tries, reductions of around 70 percent in the space required by the uncompacted trie can be expected. The quality of the compaction is shown to be insensitive to the number of nodes, while a more relevant parameter is the alphabet size of the key.

Abstract. Given an n × n binary image of white and black pixels, we present two algorithms for computing the distance transform and the nearest feature transform using the Euclidean metric. The first algorithm is a fast sequentioal O(n) time algorithm. The second is an optimal O(n) time parallel algorithm that runs on a linear array of n processors.

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