Algorithms for determining the geometrical congruity in two and three dimensions
This paper discusses the problem of determining the geometrical congruity. O(n log n) time algorithms for point sets in three dimensions and for graphs whose vertices are points in three dimensions are presented, respectively. They are based on Sugihara's algorithm for determining the congruity of polyhedra. Moreover, an O(log n) time O(n) processors parallel algorithm for graphs in two dimensions which works on a CRCW PRAM is presented. In this algorithm, the original problem is transformed into the string matching problem. All the algorithms are optimal and can be modified for computing the canonical forms.
KeywordsConvex Hull Canonical Form Time Algorithm Random Access Machine String Match Algorithm
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