The Hardness of Approximating Spanner Problems
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Geodesic Spanners on Polyhedral Surfaces
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Approximate shortest paths guided by a small index
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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We calculate a near-optimal upper bound on the weight of a graph spanner produced by the (so called) Greedy Spanner algorithm on a weighted graph. Our upper bound is independent of the magnitude of the weights in the graph, and it matches the known lower bound up to a O(log(n)) for n-vertex graphs. We also update the bound on the size of the spanner, and bound above the weight of any non-MST edge in the graph, which allows for a modification of the Greedy algorithm.