Optimal irreversible dynamos in chordal rings
Discrete Applied Mathematics - special issue on the 25th international workshop on graph theoretic concepts in computer science (WG'99)
Local majorities, coalitions and monopolies in graphs: a review
Theoretical Computer Science
Euro-Par '98 Proceedings of the 4th International Euro-Par Conference on Parallel Processing
Discrete Applied Mathematics - Special issue on international workshop on algorithms, combinatorics, and optimization in interconnection networks (IWACOIN '99)
Note: Combinatorial model and bounds for target set selection
Theoretical Computer Science
Irreversible conversion of graphs
Theoretical Computer Science
Dynamic monopolies and feedback vertex sets in hexagonal grids
Computers & Mathematics with Applications
Bounding the number of tolerable faults in majority-based systems
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Stable sets of threshold-based cascades on the erdős-rényi random graphs
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
On the non-progressive spread of influence through social networks
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Triggering cascades on undirected connected graphs
Information Processing Letters
Reversible iterative graph processes
Theoretical Computer Science
Bounding the sizes of dynamic monopolies and convergent sets for threshold-based cascades
Theoretical Computer Science
Minimum weight dynamo and fast opinion spreading
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Generalized degeneracy, dynamic monopolies and maximum degenerate subgraphs
Discrete Applied Mathematics
Hi-index | 0.00 |
We consider a well-known distributed colouring game played on a simple connected graph: initially, each vertex is coloured black or white; at each round, each vertex simultaneously recolours itself by the colour of the simple (strong) majority of its neighbours. A set of vertices M is said to be a dynamo, if starting the game with only the vertices of M coloured 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 various models and topologies.We derive tight tradeoffs between the size and the time for a number of regular graphs, including rings, complete d-ary trees, tori, wrapped butterflies, cube connected cycles and hypercubes. In addition, we determine optimal size bounds of irreversible dynamos for butterflies and shuffle-exchange using simple majority and for DeBruijn using strong majority rules. Finally, we make some observations concerning irreversible versus reversible monotone models and slow complete computations from minimal dynamos.