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) |
|---|---|
| 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 |
|---|---|
| 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
AN - SCOPUS:0036038484
SP - 705
EP - 711
BT - Conference Proceedings of the Annual ACM Symposium on Theory of Computing
ER -