Improved Approximation Bounds for the Minimum Constraint Removal Problem

Abstract In the minimum constraint removal problem, we are given a set of overlapping geometric objects as obstacles in the plane, and we want to find the minimum number of obstacles that must be removed to reach a target point t from the source point s by an obstacle-free path. The problem is known to be intractable and no sub-linear approximations are known even for simple obstacles such as rectangles and disks. The main result of our paper is an approximation framework that gives an O ( n α ( n ) ) -approximation for polygonal obstacles, where α ( n ) denotes the inverse Ackermann's function. For pseudodisks and rectilinear polygons, the same technique achieves an O ( n ) -approximation. The technique also gives O ( n ) -approximation for the minimum color path problem in graphs. We also present some inapproximability results for the geometric constraint removal problem.