Geometric spanner is a fundamental structure in computational geometry and plays an important role in many geometric networks design applications. In this paper, we consider a generalization of the classical geometric spanner problem (called segment spanner): Given a set S of disjoint 2-D segments, find a spanning network G with minimum size so that for any pair of points in S, there exists a p...

This paper is devoted to the incorporation of topological derivative like expansions of first and second order in volume and perimeter into level set methods for perimeter regularized geometric inverse problems. Based on these expansions we provide a steepest descent type and a Newton-type algorithm to force topology changes in level set methods. Numerous numerical examples are provided that sh...