Geodesic Spanners on Polyhedral Surfaces

Authors:
Sanjiv Kapoor;Xiang-Yang Li
Affiliations:
Department of Computer Science, Illinois Institute of Technology, Chicago, USA;Department of Computer Science, Illinois Institute of Technology, Chicago, USA
Venue:
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Year:
2009

Citing 7
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Abstract

In this paper we consider the problem of efficiently constructing geodesic t-spanners. We consider finding sparse spanners on the surface of a 3 dimensional polyhedron allowing for steiner vertices. If Steiner vertices are not allowed, then we establish lower bounds on the maximum node degree, depending on the spanning ratio t and also the total number of vertices of the polyhedron surface. We also consider the case of the surface of a convex polytope $\mathcal P $ with V vertices. Using its vertex set P and Steiner points, we can construct a t-spanner with a constant degree and weight O(MST(U)), where MST(U) is the minimum spanning tree on the set U of vertices on convex polytope.