Elsevier

Theoretical Computer Science

Volume 460, 16 November 2012, Pages 16-25
Theoretical Computer Science

Reversible iterative graph processes

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Abstract

Given a graph G, a function f:V(G)Z, and an initial 0/1-vertex-labelling c1:V(G){0,1}, we study an iterative 0/1-vertex-labelling process on G where in each round every vertex v changes its label if and only if at least f(v) neighbours have a different label. For special choices of the values of f, such processes model consensus issues and have been studied under names such as local majority processes or iterative polling processes in a large variety of contexts especially in distributed computing. Our contributions concern computational aspects related to the minimum cardinality rf(G) of sets of vertices with initial label 1 such that during the process on G all vertices eventually change their label to 1. Such sets are known as dynamic monopolies or dynamos for short. We establish a hardness result and describe efficient algorithms for restricted instances on paths and cycles.

Keywords

Conquest and expansion games
Local majority process
Iterative polling process
Consensus
Dynamic monopoly
Reachability problems
Finite discrete dynamical systems
Local interaction games

Cited by (0)

The results of this paper were presented as a brief announcement at DISC 2010: M.C. Dourado, L.D. Penso, D.Rautenbach, and J.L. Szwarcfiter, Brief Announcement: On Reversible and Irreversible Conversions, Distributed Computing, 24th International Symposium (DISC 2010), Cambridge, MA, USA, September 2010, LNCS 6343 (2010), 395–397.