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An optimal algorithm for the boundary of a cell in a union of rays. (English) Zbl 0697.68030

Summary: We study a cell of the subdivision induced by a union of n half-lines (or rays) in the plane. We present two results. The first one is a novel proof of the O(n) bound on the number of edges of the boundary of such a cell, which is essentially of methodological interest. The second is an algorithm for constructing the boundary of any cell, which runs in optimal \(\Theta\) (n log n) time. A by-product of our results are the notions of skeleton and of skeletal order, which may be of interest in their own right.

MSC:

68Q25 Analysis of algorithms and problem complexity
68U99 Computing methodologies and applications
68R99 Discrete mathematics in relation to computer science
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