Abstract
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.
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Carroll, D.E., Goel, A., Meyerson, A. (2006). Embedding Bounded Bandwidth Graphs into ℓ1 . In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_4
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DOI: https://doi.org/10.1007/11786986_4
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