SWAT 2014: Algorithm Theory – SWAT 2014 pp 277-281

# Additive Spanners: A Simple Construction

• Mathias Bæk Tejs Knudsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8503)

## 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).

## Keywords

Short Path Triangle Inequality SIAM Journal Simple Construction 47th IEEE Symposium
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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