Minkowski Sum Selection and Finding

Details Minkowski Sum Selection and Finding Minkowski Sum Selection and Finding

2008-09-06

arxiv.org/abs/0809.1171v1

Computer Science

Data Structures and Algorithms

23 pages, 10 figures, accepted by ISAAC 2008

Scientific paper

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 $\lambda=1$; (2) $O(n\log^2 n)$ time deterministic algorithms and expected $O(n\log n)$ time randomized algorithms for any fixed $\lambda>1$. 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 $\lambda\geq 1$.

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