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Computing dominances in $$E^ n$$. (English) Zbl 0738.68080
We show the following: Given an $$n$$-point set $$X\subseteq E^ n$$, the dominance relation on $$X$$ can be computed in time $$O(n^{3/2}M(n)^{3/2})$$, where $$M(n)$$ denotes the time needed to multiply two $$n\times n$$ matrices over $$Z_{n+1}$$.

##### MSC:
 68U05 Computer graphics; computational geometry (digital and algorithmic aspects) 68Q25 Analysis of algorithms and problem complexity
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##### References:
 [1] Coppersmith, D.; Winograd, S., Matrix multiplication via arithmetic progressions, J. symbolic comput., 9, 3, 251-280, (1990) · Zbl 0702.65046 [2] Preparata, F.; Shamos, M.I., Computational geometry - an introduction, (1985), Springer Berlin · Zbl 0759.68037 [3] S. Suri, Private communication, 1990
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