Abstract
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.
Original language | English (US) |
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Title of host publication | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |
Pages | 705-711 |
Number of pages | 7 |
State | Published - 2002 |
Event | Proceedings of the 34th Annual ACM Symposium on Theory of Computing - Montreal, Que., Canada Duration: May 19 2002 → May 21 2002 |
Other
Other | Proceedings of the 34th Annual ACM Symposium on Theory of Computing |
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Country | Canada |
City | Montreal, Que. |
Period | 5/19/02 → 5/21/02 |
ASJC Scopus subject areas
- Software
Cite this
Girth and Euclidean distortion. / Linial, Nathan; Magen, Avner; Naor, Assaf.
Conference Proceedings of the Annual ACM Symposium on Theory of Computing. 2002. p. 705-711.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
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
UR - http://www.scopus.com/inward/citedby.url?scp=0036038484&partnerID=8YFLogxK
M3 - Conference contribution
SP - 705
EP - 711
BT - Conference Proceedings of the Annual ACM Symposium on Theory of Computing
ER -