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Proceedings of the Seventeenth Annual Symposium on Computational Geometry, (SCG '01), June 3-5, 2001, Medford, Massachusetts, USAsponsored by the ACM Special Interest Group for Graphics and Algorithms and Computation TheoryProc. of 17th Annual ACM Symposium on Computational GeometryWe 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 $tilde{O}( n^{8/7}k^{1/7} + n k^{1/3})$

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