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SAGA
2007
Springer

Approximate Discovery of Random Graphs

8 years 11 months ago
Approximate Discovery of Random Graphs
In the layered-graph query model of network discovery, a query at a node v of an undirected graph G discovers all edges and non-edges whose endpoints have different distance from v. We study the number of queries at randomly selected nodes that are needed for approximate network discovery in Erd˝os-R´enyi random graphs Gn,p. We show that a constant number of queries is sufficient if p is a constant, while Ω(nα ) queries are needed if p = nε /n, for arbitrarily small choices of ε = 3/(6 · i + 5) with i ∈ N. Note that α > 0 is a constant depending only on ε. Our proof of the latter result yields also a somewhat surprising result on pairwise distances in random graphs which may be of independent interest: We show that for a random graph Gn,p with p = nε /n, for arbitrarily small choices of ε > 0 as above, in any constant cardinality subset of the nodes the pairwise distances are all identical with high probability.
Thomas Erlebach, Alexander Hall, Matús Miha
Added 09 Jun 2010
Updated 09 Jun 2010
Type Conference
Year 2007
Where SAGA
Authors Thomas Erlebach, Alexander Hall, Matús Mihalák
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