Chew shows that the L 1 Delaunay triangulation of S is a Euclidean p 10 spanner. Lower bounds for computing geometric spanners and approximate shortest paths . It gives a k fault tolerant t spanner, in which the degree of each vertex is bounded by a constant, and whose weight is proportional to the weight of a minimum spanning tree. Chen et al. Therefore, the result of Theorem 4 is optimal for constant values of k.
Some interesting problems remain to be solved.
D. Z. Chen, G. Das, and M. Smid. Lower bounds for computing geometric spanners and approximate shortest paths . We assume that the reader is familiar with the algebraic computation tree model. D. Z. Chen, G. Das, and M. Smid. Lower bounds for computing geometric spanners and approximate shortest paths .