Feasibility of the Exact Geometric Computation Paradigm for Largest Empty Anchored Cylinder Computation in the Plane

In the largest empty anchored cylinder problem one is looking for a ray anchored at the origin that maximizes the minimum (weighted) distance to a given set of points. For a set of n points in the plane, Follert et al. presented an optimal O(n log n) algorithm. We analyze the algebraic degree of the computations involved in their algorithm and show that it is much smaller than it looks at first sight. Indeed, a deliberate implementation of the optimal algorithm surprisingly avoids irrational number computations at all. Thus efficient exact geometric computation becomes feasible for this problem.