TY - JOUR
T1 - Testing the expansion of a graph
AU - Nachmias, Asaf
AU - Shapira, Asaf
N1 - Funding Information:
∗ Corr esponding author. E-mail address: [email protected] (A. Nachmias). 1 Research supported in part by NSF Grant #DMS-0605166. 2 Supported in part by NSF Grant DMS-0901355.
PY - 2010/4
Y1 - 2010/4
N2 - 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].
AB - 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].
UR - http://www.scopus.com/inward/record.url?scp=76349097997&partnerID=8YFLogxK
U2 - 10.1016/j.ic.2009.09.002
DO - 10.1016/j.ic.2009.09.002
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AN - SCOPUS:76349097997
SN - 0890-5401
VL - 208
SP - 309
EP - 314
JO - Information and Computation
JF - Information and Computation
IS - 4
ER -