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 proximity-preserving labeling scheme. It is shown that for the class of n-vertex weighted trees with M-bit edge weights, there exists such a proximity-preserving labeling scheme using O(M log n + log2 n) bit labels. For the family of all n-vertex unweighted graphs, a labeling scheme is proposed that using O(log2 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(log3 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, proximity-preserving 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.
Supported in part by grants from the Israel Science Foundation and from the Israel Ministry of Science and Art.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Baruch Awerbuch, Shay Kutten, and David Peleg. On buffer-economical store-and-forward deadlock prevention. In Proc. INFOCOM, pages 410–414, 1991. 36, 36, 36
Baruch Awerbuch and David Peleg. Routing with polynomial communication-space trade-off. SIAM J. on Discr. Math., pages 151–162, 1992. 40, 41
J. Bourgain. On Lipschitz embeddings of finite metric spaces in Hilbert spaces. Israel J. Math., pages 46–52, 1985. 40
Melvin A. Breuer. Coding the vertexes of a graph. IEEE Trans. on Information Theory, IT-12:148–153, 1966. 31
Melvin A. Breuer and Jon Folkman. An unexpected result on coding the vertices of a graph. J. of Mathematical Analysis and Applications, 20:583–600, 1967. 31, 31
Greg N. Frederickson and Ravi Janardan. Space-efficient message routing in c-decomposable networks. SIAM J. on Computing, pages 164–181, 1990. 32
Cyril Gavoille, David Peleg, Stéphane Pérennes, and Ran Raz. Distance labeling in graphs. In preparation, 1999. 40, 40
Y. Hassin. Private communication, 1999. 40
P. Indyk and R. Motwani. Approximate nearest neighbors: towards removing the curse of dimensionality. In Proc. 30th ACM Symp. on Theory of Computing, 1998. 40
Sampath Kannan, Moni Naor, and Steven Rudich. Implicit representation of graphs. In Proc. 20th ACM Symp. on Theory of Computing, pages 334–343, May 1988. 31
N. Linial, E. London, and Y. Rabinovich. The geometry of graphs and some of its algorithmic applications. Combinatorica, 15:215–245, 1995. 40, 40
R.B. Tan. Private communication, 1997. 40
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Peleg, D. (1999). Proximity-Preserving Labeling Schemes and Their Applications. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds) Graph-Theoretic Concepts in Computer Science. WG 1999. Lecture Notes in Computer Science, vol 1665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46784-X_5
Download citation
DOI: https://doi.org/10.1007/3-540-46784-X_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66731-5
Online ISBN: 978-3-540-46784-7
eBook Packages: Springer Book Archive