The first polynomial self-stabilizing 1-maximal matching algorithm for general graphs

Johanne Cohen, Jonas Lefèvre, Khaled Maâmra, George Manoussakis, Laurence Pilard

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We present the first polynomial self-stabilizing algorithm for finding a 1-maximal matching in a general graph. The previous best known algorithm has been presented by Manne et al. [20]and we show in this paper it has a sub-exponential time complexity under the distributed adversarial daemon. Our new algorithm is an adaptation of the Manne et al. algorithm and works under the same daemon, but with a complexity in O(m×n2) moves, with n is the number of nodes and m is the number of edges. This is the first self-stabilizing algorithm that solve this problem with a polynomial complexity. Moreover, our algorithm only needs one more boolean variable than the previous one.

Original languageEnglish
Pages (from-to)54-78
Number of pages25
JournalTheoretical Computer Science
StatePublished - 23 Aug 2019
Externally publishedYes


  • 1-maximal matching
  • Self-stabilization
  • [Formula presented]-approximation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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