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.

• Type: Conference
• Year: 2009
• Where: CCCG
• Authors: Joondong Kim, Joseph S. B. Mitchell, Jingyu Zou
• Keywords: CCCG 2007, CCCG 2009, Maximum Flow Problem, Polygonal Domain, Polygonal Domain P