Approximate Discovery of Random Graphs

Thomas Erlebach, Alexander Hall, Matúš Mihalák

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

Abstract

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 Erdos-Renyi random graphs G_(n,p). We show that a constant number of queries is sufficient if p is a constant, while Ω(n^α) queries are needed if p = n^ε/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 G_(n,p) with p = n^ε/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.
Original languageEnglish
Title of host publicationProceedings of the 4th Symposium on Stochastic Algorithms, Foundations, and Applications (SAGA)
Pages82-92
Number of pages11
DOIs
Publication statusPublished - 2007
Externally publishedYes

Cite this

Erlebach, T., Hall, A., & Mihalák, M. (2007). Approximate Discovery of Random Graphs. In Proceedings of the 4th Symposium on Stochastic Algorithms, Foundations, and Applications (SAGA) (pp. 82-92) https://doi.org/10.1007/978-3-540-74871-7_8