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

概要

論文の詳細を見る
Proceedings of the Seventeenth Annual Symposium on Computational Geometry, (SCG '01), June 3-5, 2001, Medford, Massachusetts, USA / sponsored by the ACM Special Interest Group for Graphics and Algorithms and Computation TheoryWe give an algorithm to compute all the local peaks in the $k$-level o f 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 $\tilde{O}( n^{8/7}k^{1/7} + n k^{1/3})$.