On an application of convexity to discrete systems
Discrete Applied Mathematics
On pre-periods of discrete influence systems
Discrete Applied Mathematics
Size bounds for dynamic monopolies
Discrete Applied Mathematics
Fault-local distributed mending
Journal of Algorithms
An improved testing scheme for catastrophic fault patterns
Information Processing Letters
Mining the network value of customers
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Distributed probabilistic polling and applications to proportionate agreement
Information and Computation
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)
Dynamic monopolies of constant size
Journal of Combinatorial Theory Series B
Local majorities, coalitions and monopolies in graphs: a review
Theoretical Computer Science
Computational complexity of neural networks: a survey
Nordic Journal of Computing
On Majority Voting Games in Trees
SOFSEM '01 Proceedings of the 28th Conference on Current Trends in Theory and Practice of Informatics Piestany: Theory and Practice of Informatics
The power of small coalitions in graphs
Discrete Applied Mathematics
Maximizing the spread of influence through a social network
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
On time versus size for monotone dynamic monopolies in regular topologies
Journal of Discrete Algorithms
Listen to Your Neighbors: How (Not) to Reach a Consensus
SIAM Journal on Discrete Mathematics
Information Processing Letters
Complexity of reachability problems for finite discrete dynamical systems
Journal of Computer and System Sciences
Discrete Applied Mathematics
On the Approximability of Influence in Social Networks
SIAM Journal on Discrete Mathematics
Convergence to Equilibrium in Local Interaction Games
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Random Structures & Algorithms
Irreversible conversion of graphs
Theoretical Computer Science
| Hi-index | 5.23 |
Given a graph G, a function f:V(G)-Z, and an initial 0/1-vertex-labelling c"1: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 r"f(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.