Approximating maximum flow in polygonal domains using spanners

We study a maximum flow problem in a polygonal domain P: Determine the maximum number of disjoint thick paths (of specified width w) through P from a source edge to a sink edge of P. We show that Euclidean spanners offer a means of computing approximately optimal solutions. For a polygonal domain with n vertices and h point holes, we give a 1=2-approximation algorithm that runs in time O(n + h log(nh)); this is to be contrasted with the known exact methods that take time O(nh+n log n). Further, we show experimentally that using a spanner (e.g., Delaunay graph) yields approximation ratios very close to one.