Testing the expansion of a graph

Asaf Nachmias*, Asaf Shapira

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

We study the problem of testing the expansion of graphs with bounded degree d in sublinear time. A graph is said to be an α-expander if every vertex set U ⊂ V of size at most frac(1, 2) | V | has a neighborhood of size at least α | U |. We show that the algorithm proposed by Goldreich and Ron [9] (ECCC-2000) for testing the expansion of a graph distinguishes with high probability between α-expanders of degree bound d and graphs which are -far from having expansion at least Ω (α2). This improves a recent result of Czumaj and Sohler [3] (FOCS-07) who showed that this algorithm can distinguish between α-expanders of degree bound d and graphs which are -far from having expansion at least Ω (α2 / log n). It also improves a recent result of Kale and Seshadhri [12] (ECCC-2007) who showed that this algorithm can distinguish between α-expanders and graphs which are -far from having expansion at least Ω (α2) with twice the maximum degree. Our methods combine the techniques of [3], [9] and [12].

Original languageEnglish
Pages (from-to)309-314
Number of pages6
JournalInformation and Computation
Volume208
Issue number4
DOIs
StatePublished - Apr 2010
Externally publishedYes

Funding

FundersFunder number
National Science FoundationDMS-0901355
Directorate for Mathematical and Physical Sciences0901355, 0605166

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