TY - JOUR
T1 - Girth and Euclidean distortion
AU - Linial, Nathan
AU - Magen, Avner
AU - Naor, Assaf
PY - 2002
Y1 - 2002
N2 - In this paper we partially prove a conjecture that was raised by Linial, London and Rabinovich in [11]. Let G be a k-regular graph, k ≥ 3, with girth g. We show that every embedding f : G → ℓ2 has distortion Ω(√g). The original conjecture which remains open is that the Euclidean distortion is bounded below by Ω(g). Two proofs are given, one based on semi-definite programming, and the other on Markov Type, a concept that considers random walks on metrics.
AB - In this paper we partially prove a conjecture that was raised by Linial, London and Rabinovich in [11]. Let G be a k-regular graph, k ≥ 3, with girth g. We show that every embedding f : G → ℓ2 has distortion Ω(√g). The original conjecture which remains open is that the Euclidean distortion is bounded below by Ω(g). Two proofs are given, one based on semi-definite programming, and the other on Markov Type, a concept that considers random walks on metrics.
UR - http://www.scopus.com/inward/record.url?scp=0036038484&partnerID=8YFLogxK
U2 - 10.1145/509907.510009
DO - 10.1145/509907.510009
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AN - SCOPUS:0036038484
SN - 0734-9025
SP - 705
EP - 711
JO - Conference Proceedings of the Annual ACM Symposium on Theory of Computing
JF - Conference Proceedings of the Annual ACM Symposium on Theory of Computing
T2 - Proceedings of the 34th Annual ACM Symposium on Theory of Computing
Y2 - 19 May 2002 through 21 May 2002
ER -