About Randomised Distributed Graph Colouring and Graph Partition Algorithms

Yves Métivier (1) , John Michael Robson (1) , Nasser Saheb-Djahromi (1) , Akka Zemmari (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We present and analyse a very simple randomised distributed vertex colouring algorithm for arbitrary graphs of size $n$ that halts in time $O(\log n)$ with probability $1-o(n^{-1}).$ Each message containing $1$ bit, its bit complexity per channel is $O(\log n)$. >From this algorithm, we deduce and analyse a randomised distributed vertex colouring algorithm for arbitrary graphs of maximum degree $\Delta$ and size $n$ that uses at most $\Delta+1$ colours and halts in time $O(\log n)$ with probability $1-o(n^{-1}).$ We also obtain a partition algorithm for arbitrary graphs of size $n$ that builds a spanning forest in time $O(\log n)$ with probability $1-o(n^{-1})$. We study some parameters such as the number, the size and the radius of trees of the spanning forest

Mots clés: Bit Complexity; Randomised Distributed Graph Algorithm; Colouring; Graph Partition; Probabilistic Analysis; Bit Complexity.

Domaines: Autre [cs.OH]

Yves Métivier, John Michael Robson, Nasser Saheb-Djahromi, Akka Zemmari. About Randomised Distributed Graph Colouring and Graph Partition Algorithms. Information and Computation, 2010, 208 (2), pp.1296-1304. ⟨10.1016/j.ic.2010.07.001⟩. ⟨hal-00515904⟩