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FOCS
2006
IEEE

Lower Bounds for Additive Spanners, Emulators, and More

9 years 5 months ago
Lower Bounds for Additive Spanners, Emulators, and More
An additive spanner of an unweighted undirected graph G with distortion d is a subgraph H such that for any two vertices u, v ∈ G, we have δH(u, v) ≤ δG(u, v) + d. For every k = O( ln n ln ln n ), we construct a graph G on n vertices for which any additive spanner of G with distortion 2k − 1 has Ω(1 k n1+1/k ) edges. This matches the lower bound previously known only to hold under a 1963 conjecture of Erd¨os. We generalize our lower bound in a number of ways. First, we consider graph emulators introduced by Dor, Halperin, and Zwick (FOCS, 1996), where an emulator of an unweighted undirected graph G with distortion d is like an additive spanner except H may be an arbitrary weighted graph such that δG(u, v) ≤ δH(u, v) ≤ δG(u, v) + d. We show a lower bound of Ω( 1 k2 n1+1/k ) edges for distortion-(2k − 1) emulators. These are the first non-trivial bounds for k > 3. Second, we parameterize our bounds in terms of the minimum degree of the graph. Namely, for minimu...
David P. Woodruff
Added 11 Jun 2010
Updated 11 Jun 2010
Type Conference
Year 2006
Where FOCS
Authors David P. Woodruff
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