Notes on computing peaks in k-levels and parametric spanning trees

Details Notes on computing peaks in k-levels and parametric spanning trees Notes on computing peaks in k-levels and parametric spanning trees

2001-03-29

arxiv.org/abs/cs/0103024v1

Computer Science

Computational Geometry

ACM SCG'01

Scientific paper

We give an algorithm to compute all the local peaks in the $k$-level of an arrangement of $n$ lines in $O(n \log n) + \tilde{O}((kn)^{2/3})$ time. We can also find $\tau$ largest peaks in $O(n \log ^2 n) + \tilde{O}((\tau n)^{2/3})$ time. Moreover, we consider the longest edge in a parametric minimum spanning tree (in other words, a bottleneck edge for connectivity), and give an algorithm to compute the parameter value (within a given interval) maximizing/minimizing the length of the longest edge in MST. The time complexity is $\tilde{O}(n^{8/7}k^{1/7} + n k^{1/3})$

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