Algorithms for ball hulls and ball intersections in strictly convex normed planes

Abstract

Extending results of Hershberger and Suri for the Euclidean plane, we show that ball hulls and ball intersections of sets of $n$ points in strictly convex normed planes can be constructed in $O(n \log n)$ time. In addition, we confirm that, like in the Euclidean subcase, the $2$-center problem with constrained circles can be solved also for strictly convex normed planes in $O(n^2)$ time. Some ideas for extending these results to more general types of normed planes are also presented.