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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Pages (from-to) | 705-711 |
Number of pages | 7 |
Journal | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |
DOIs | |
State | Published - 2002 |
Externally published | Yes |
Event | Proceedings of the 34th Annual ACM Symposium on Theory of Computing - Montreal, Que., Canada Duration: May 19 2002 → May 21 2002 |
All Science Journal Classification (ASJC) codes
- Software