Graphs with small bandwidth and cutwidth
Discrete Mathematics
Optimal embedding of complete binary trees into lines and grids
Journal of Parallel and Distributed Computing - Parallel and distributed data structures
Embedding tree metrics into low dimensional Euclidean spaces
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Low-distortion embeddings of general metrics into the line
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Approximation algorithms for low-distortion embeddings into low-dimensional spaces
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
D-width, metric embedding, and their connections
D-width, metric embedding, and their connections
Optimal distortion embedding of complete binary trees into lines
Information Processing Letters
Hi-index | 0.89 |
In this paper, we show how we can derive lower bounds and also compute the exact distortion for the line embeddings of some special metrics, especially trees and graphs with certain structure. Using linear programming to formulate a simpler version of the problem gives an interesting intuition and direction concerning the computation of general lower bounds for distortion into the line. We also show that our lower bounds on special cases of metrics are a lot better than previous lower bounds.