Graphs with small bandwidth and cutwidth
Discrete Mathematics
Approximating the bandwidth via volume respecting embeddings (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Small distortion and volume preserving embeddings for planar and Euclidean metrics
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Embedding k-outerplanar graphs into ℓ1
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On average distortion of embedding metrics into the line and into L1
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Cuts, Trees and -Embeddings of Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Approximation algorithms for low-distortion embeddings into low-dimensional spaces
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Bandwidth and low dimensional embedding
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Bandwidth and low dimensional embedding
Theoretical Computer Science
| Hi-index | 0.00 |
We introduce the first embedding of graphs of low bandwidth into ℓ1, with distortion depending only upon the bandwidth. We extend this result to a new graph parameter called tree-bandwidth, which is very similar to (but more restrictive than) treewidth. This represents the first constant distortion embedding of a non-planar class of graphs into ℓ1. Our results make use of a new technique that we call iterative embedding in which we define coordinates for a small number of points at a time.