Mathematical Foundations of Computer Science 2000
Volume 1893 of the series Lecture Notes in Computer Science pp 579588
Informative Labeling Schemes for Graphs
 David PelegAffiliated withThe Weizmann Institute of Science, Department of Computer Science and Applied Mathematics
Abstract
This paper introduces and studies the notion of informative labeling schemes for arbitrary graphs. Let f(W) be a function on subsets of vertices W. An f labeling scheme labels the vertices of a weighted graph G in such a way that f(W) can be inferred efficiently for any vertex subset W of G by merely inspecting the labels of the vertices of W, without having to use any additional information sources.
The paper develops f labeling schemes for some functions f over the class of nvertex trees, including SepLevel, the separation level of any two vertices in the tree, LCA, the least common ancestor of any two vertices, and Center, the center of any three given vertices in the tree. These schemes use O(log^{2} n)bit labels, which is asymptotically optimal.
We then turn to weighted graphs and consider the function Steiner(W), denoting the weight of the Steiner tree spanning the vertices of W in the graph. For nvertex weighted trees with Mbit edge weights, it is shown that there exists a Steiner labeling scheme using O((M+log n) log n) bit labels, which is asymptotically optimal. In the full paper it is shown that for the class of arbitrary nvertex graphs with Mbit edge weights, there exists an approximate Steiner labeling scheme, providing an estimate (up to a logarithmic factor) for Steiner(W) using O((M + logn) log^{2} n) bit labels.
 Title
 Informative Labeling Schemes for Graphs
 Book Title
 Mathematical Foundations of Computer Science 2000
 Book Subtitle
 25th International Symposium, MFCS 2000 Bratislava, Slovakia, August 28 – September 1, 2000 Proceedings
 Pages
 pp 579588
 Copyright
 2000
 DOI
 10.1007/3540446125_53
 Print ISBN
 9783540679011
 Online ISBN
 9783540446125
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1893
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
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 Editors

 Mogens Nielsen ^{(4)}
 Branislav Rovan ^{(5)}
 Editor Affiliations

 4. Department of Computer Science, University of Aarhus
 5. Department of Computer Sciene, Comenius University
 Authors

 David Peleg ^{(6)}
 Author Affiliations

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