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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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