Characterization of graphs and digraphs with small process number

David Coudert (1) , Jean-Sébastien Sereni (2, 3)

1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
3 KAM - Department of Applied Mathematics (KAM)

We introduce the process number of a digraph as a tool to study rerouting issues in \wdm networks. This parameter is closely related to the vertex separation (or pathwidth). We consider the recognition and the characterization of (di)graphs with small process number. In particular, we give a linear time algorithm to recognize (and process) graphs with process number at most 2, along with a characterization in terms of forbidden minors, and a structural description. As for digraphs with process number 2, we exhibit a characterization that allows one to recognize (and process) them in polynomial time.

Domaines: Réseaux et télécommunications [cs.NI]

David Coudert, Jean-Sébastien Sereni. Characterization of graphs and digraphs with small process number. Discrete Applied Mathematics, 2011, 159 (11), pp.1094-1109. ⟨10.1016/j.dam.2011.03.010⟩. ⟨inria-00587717⟩