  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 $\tilde{O}(n^{8/7}k^{1/7} + n k^{1/3})$
