Continuous Optimization The maximin line problem with regional demand

Given a family P ¼f P 1; ... ; P mg of m polygonal regions (possibly intersecting) in the plane, we consider the problem of locating a straight line ' intersecting the convex hull of P and such that mink d(Pk, ') is maximal. We give an algorithm that solves the problem in time O((m2 + n log m) log n) using O(m2 + n) space, where n is the total number of vertices of