Proximity-preserving labeling schemes

David Peleg

Research output: Contribution to journalArticlepeer-review

100 Scopus citations


This article 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 · n1/k) bit labels can provide approximate estimates to the distance, which are accurate up to a factor of √8k. 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.)

Original languageEnglish
Pages (from-to)167-176
Number of pages10
JournalJournal of Graph Theory
Issue number3
StatePublished - Mar 2000
Externally publishedYes


  • Approximate-distance
  • Graph representations
  • Labeling schemes


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