Notes on computing peaks in klevels and parametric spanning trees
Abstract
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 $\tilde{O}(n^{8/7}k^{1/7} + n k^{1/3})$
 Publication:

arXiv eprints
 Pub Date:
 March 2001
 arXiv:
 arXiv:cs/0103024
 Bibcode:
 2001cs........3024K
 Keywords:

 Computational Geometry;
 Data Structures and Algorithms;
 F2.2
 EPrint:
 ACM SCG'01