On time versus size for monotone dynamic monopolies in regular topologies

: We consider a well known distributed coloring game played on a simple connected graph: initially, each vertex is colored black or white; at each round, each vertex simultaneously recolors itself by the color of the simple (strong) majority of its neighbours. A set of vertices is said to be a dynamo, if starting the game with only the vertices of colored black, the computation eventually reaches an all-black configuration. The importance of this game follows from the fact that it models the spread of faults in point-to-point systems with majority-based voting; in particular, dynamos correspond to those sets of initial failures which will lead the entire system to fail. Investigations on dynamos have been extensive but restricted to establishing tight bounds on the size (i.e. how small a dynamic monopoly might be). In this paper we start to study dynamos systematically with respect to both the size and the time (i.e. how many rounds are needed to reach all-black configuration) in vari...

• Type: Conference
• Year: 2000
• Where: SIROCCO
• Authors: Paola Flocchini, Rastislav Kralovic, Alessandro Roncato, Peter Ruzicka, Nicola Santoro
• Keywords: All-black Configuration, Optimal Size Bounds, Simple Connected Graph, SIROCCO 2000, SIROCCO 2007