Average case analysis for tree labelling schemes

Ming-Yang Kao, Xiang Yang Li*, Weizhao Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We study how to label the vertices of a tree in such a way that we can decide the distance of two vertices in the tree given only their labels. Gavoille et al. proved that for any such distance labelling scheme, the maximum label length is at least frac(1, 8) log2 n - O (log n) bits, where n is the number of vertices in the input tree T. They also gave a separator-based labelling scheme that has the optimal label length Θ (log n {dot operator} log (Hn (T))), where Hn (T) is the height of T. We present two distance labelling schemes, namely, the backbone-based scheme and rake-based scheme, which also achieve the optimal label length. The two schemes always perform at least as well as the separator scheme. Furthermore, the rake-based scheme has a much smaller expected label length under certain tree distributions. With these new schemes, we also can find the least common ancestor of any two vertices based on their labels only.

Original languageEnglish (US)
Pages (from-to)271-291
Number of pages21
JournalTheoretical Computer Science
Issue number3
StatePublished - Jun 9 2007


  • Average case analysis
  • Separator
  • Tree labelling

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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