On an application of convexity to discrete systems
Discrete Applied Mathematics
The number of fixed points of the majority rule
Discrete Mathematics
On a paper of Agur, Fraenkel and Klein
Discrete Mathematics
The r-majority vote action on 0-1 sequences
Discrete Mathematics
Parametrization for stationary patterns of the r-majority operators on 0-1 sequences
Discrete Mathematics
Randomized algorithms
Almost exact minimum feedback vertex set in meshes and butterflies
Information Processing Letters
Size bounds for dynamic monopolies
Discrete Applied Mathematics
The majority action on infinite graphs: strings and puppets
Discrete Mathematics
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
Majority Consensus and the Local Majority Rule
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
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
Discrete Applied Mathematics - Special issue on international workshop on algorithms, combinatorics, and optimization in interconnection networks (IWACOIN '99)
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Decycling Cartesian Products of Two Cycles
SIAM Journal on Discrete Mathematics
On the approximability of influence in social networks
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Discrete Applied Mathematics
Theoretical Computer Science
Convergence to Equilibrium in Local Interaction Games
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Note: Combinatorial model and bounds for target set selection
Theoretical Computer Science
Bootstrap percolation in high dimensions
Combinatorics, Probability and Computing
Spreading of Messages in Random Graphs
Theory of Computing Systems
Variants of spreading messages
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Bounding the number of tolerable faults in majority-based systems
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
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Consider the following reversible cascade on the Erdős-Rényi random graph G(n,p). In round zero, a set of vertices, called the seeds, are active. For a given ρ∈( 0,1 ], a non-isolated vertex is activated (resp., deactivated) in round t∈ℤ+ if the fraction f of its neighboring vertices that were active in round t−1 satisfies f≥ρ (resp., fρ). An irreversible cascade is defined similarly except that active vertices cannot be deactivated. A set of vertices, S, is said to be stable if no vertex will ever change its state, from active to inactive or vice versa, once the set of active vertices equals S. For both the reversible and the irreversible cascades, we show that for any constant ε0, all p∈[ (1+ε) (ln (e/ρ))/n,1 ] and with probability 1−n−Ω(1), every stable set of G(n,p) has size O(⌈ρn⌉) or n−O(⌈ρn⌉).