Abstract
We consider additive spanners of unweighted undirected graphs. Let G be a graph and H a subgraph of G. The most naïve way to construct an additive k-spanner of G is the following: As long as H is not an additive k-spanner repeat: Find a pair (u,v) ∈ H that violates the spanner-condition and a shortest path from u to v in G. Add the edges of this path to H.
We show that, with a very simple initial graph H, this naïve method gives additive 6- and 2-spanners of sizes matching the best known upper bounds. For additive 2-spanners we start with H = ∅ and end with O(n 3/2) edges in the spanner. For additive 6-spanners we start with H containing \(\lfloor n^{1/3} \rfloor\) arbitrary edges incident to each node and end with a spanner of size O(n 4/3).
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Knudsen, M.B.T. (2014). Additive Spanners: A Simple Construction. In: Ravi, R., Gørtz, I.L. (eds) Algorithm Theory – SWAT 2014. SWAT 2014. Lecture Notes in Computer Science, vol 8503. Springer, Cham. https://doi.org/10.1007/978-3-319-08404-6_24
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DOI: https://doi.org/10.1007/978-3-319-08404-6_24
Publisher Name: Springer, Cham
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