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.
The research of authors is partially supported by NSF CNS-0916743, NSF CNS-0832120, National Natural Science Foundation of China under Grant No. 60828003, Hong Kong CERG under Grant PolyU-5232/07E, and Hong Kong RGC HKUST 6169/07.
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Kapoor, S., Li, XY. (2009). Geodesic Spanners on Polyhedral Surfaces. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_23
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DOI: https://doi.org/10.1007/978-3-642-10631-6_23
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