Abstract
We give two optimal parallel algorithms for constructing the arrangement ofn lines in the plane. The first nethod is quite simple and runs inO(log2 n) time usingO(n 2) work, and the second method, which is more sophisticated, runs inO(logn) time usingO(n 2) work. This second result solves a well-known open problem in parallel computational geometry, and involves the use of a new algorithmic technique, the construction of an ɛ-pseudocutting. Our results immediately imply that the arrangement ofn hyperplanes in ℝd inO(logn) time usingO(n d) work, for fixedd, can be optimally constructed. Our algorithms are for the CREW PRAM.
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