Codes over Trees

Lev Yohananov, Eitan Yaakobi

Research output: Contribution to journalArticlepeer-review


In graph theory, a tree is one of the more popular families of graphs with a wide range of applications in computer science as well as many other related fields. While there are several distance measures over the set of all trees, we consider here the one which defines the so-called tree distance, defined by the minimum number of edit operations, of removing and adding edges, in order to change one tree into another. From a coding theoretic perspective, codes over the tree distance are used for the correction of edge erasures and errors. However, studying this distance measure is important for many other applications that use trees and properties on their locality and the number of neighbor trees. Under this paradigm, the largest size of code over trees with a prescribed minimum tree distance is investigated. Upper bounds on these codes as well as code constructions are presented. A significant part of our study is dedicated to the problem of calculating the size of the ball of trees of a given radius. These balls are not regular and thus we show that while the star tree has asymptotically the smallest size of the ball, the maximum is achieved for the path tree.

Original languageEnglish
Article number9350287
Pages (from-to)3599-3622
Number of pages24
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - 1 Jun 2021
Externally publishedYes


  • Cayley's formula
  • Codes over graphs
  • Prüfer sequences
  • tree distance
  • tree edit distance

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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