ProximityPreserving Labeling Schemes and Their Applications
 David Peleg
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Abstract
This paper considers informative labeling schemes for graphs. Specifically, the question introduced is whether it is possible to label the vertices of a graph with short labels in such a way that the distance between any two vertices can be inferred from inspecting their labels. A labeling scheme enjoying this property is termed a proximitypreserving labeling scheme. It is shown that for the class of nvertex weighted trees with Mbit edge weights, there exists such a proximitypreserving labeling scheme using O(M log n + log^{2} n) bit labels. For the family of all nvertex unweighted graphs, a labeling scheme is proposed that using O(log^{2} n · k · n ^{1/k }) bit labels can provide approximate estimates to the distance, which are accurate up to a factor of √κ. In particular, using O(log^{3} n) bit labels the scheme can provide estimates accurate up to a factor of √2 log n. (For weighted graphs, one of the log n factors in the label size is replaced by a factor logarithmic in the network’s diameter.) In addition to their theoretical interest, proximitypreserving labeling systems seem to have some relevance in the context of communication networks. We illustrate this by proposing a potential application of our labeling schemes to efficient distributed connection setup in circuit switched networks.
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 Title
 ProximityPreserving Labeling Schemes and Their Applications
 Book Title
 GraphTheoretic Concepts in Computer Science
 Book Subtitle
 25th International Workshop, WG’99 Ascona, Switzerland, June 17–19, 1999 Proceedings
 Pages
 pp 3041
 Copyright
 1999
 DOI
 10.1007/354046784X_5
 Print ISBN
 9783540667315
 Online ISBN
 9783540467847
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1665
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 Editors

 Peter Widmayer ^{(4)}
 Gabriele Neyer ^{(4)}
 Stephan Eidenbenz ^{(4)}
 Editor Affiliations

 4. Institute for Theoretical Computer Science ETH Zürich ETH Zentrum
 Authors

 David Peleg ^{(5)}
 Author Affiliations

 5. Department of Applied Mathematics and Computer Science, The Weizmann Institute, Rehovot, 76100, Israel
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