Area-Preserving Subdivision Simplification with Topology Constraints: Exactly and in Practice

Abstract

Given a planar subdivision and a set of points, we want to simplify the subdivision by removing vertices of degree 2. The vertices should be removed in such a way that all points remain in their respective faces, the area of any face changes by a factor of at most δ and the distance of the resulting lines to the original ones is at most ε.While inapproximability carries over from less general problems, we present an heuristic approach which solves continental sized instances in seconds. For citysized instances we can compute optimal results via Integer-Linear-Programming and show, that our algorithm provides close-to-optimal results.