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arXiv · 0809.1171

Minkowski Sum Selection and Finding

Cheng-Wei Luo·Hsiao-Fei Liu·Peng-An Chen·Kun-Mao Chao
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Abstract

For the \textsc{Minkowski Sum Selection} problem with linear objective functions, we obtain the following results: (1) optimal $O(n\log n)$ time algorithms for $λ=1$; (2) $O(n\log^2 n)$ time deterministic algorithms and expected $O(n\log n)$ time randomized algorithms for any fixed $λ>1$. For the \textsc{Minkowski Sum Finding} problem with linear objective functions or objective functions of the form $f(x,y)=\frac{by}{ax}$, we construct optimal $O(n\log n)$ time algorithms for any fixed $λ\geq 1$.

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Cheng-Wei Luo, Hsiao-Fei Liu, Peng-An Chen, Kun-Mao Chao. 2008-09-06. Minkowski Sum Selection and Finding. https://arxiv.org/abs/0809.1171

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