Exact and approximation algorithms for computing optimal fat decompositions

The minimum α-fat decomposition problem is the problem of decomposing a simple polygon into fewest subpolygons, each with aspect ratio at most α, for a given α > 0. The main result in the paper is a polynomial time algorithm that solves the version of this problem that disallows Steiner points. The algorithm returns an optimal α-fat decomposition, if there is one, and reports failure otherwise. We also devise a faster approximation algorithm that produces, for any ε > 0, an (α + ε)-fat decomposition with as few polygons as an optimal α-fat decomposition.  2004 Elsevier B.V. All rights reserved.