Bounded-degree polyhedronization of point sets
In 1994 Grnbaum showed that, given a point set S  in R3 R 3 , it is always possible to construct a polyhedron whose vertices are exactly S. Such a polyhedron is called a polyhedronization of S . Agarwal et al. extended this work in 2008 by showing that there always exists a polyhedronization that can be decomposed into a union of tetrahedra (tetrahedralizable). In the same work they introduced the notion of a serpentine polyhedronization for which the dual of its tetrahedralization is a chain. In this work we present a randomized algorithm running in O ( n log 6 n ) expected time which constructs a serpentine polyhedronization that has vertices with degree at most 7, answering an open question by Agarwal et al.
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