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,
Graph Immunity Against Local Influence
Graph Immunity Against Local Influence
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
Bootstrap Percolation on Infinite Trees and Non-Amenable Groups
Combinatorics, Probability and Computing
On the submodularity of influence in social networks
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Discrete Applied Mathematics
Majority bootstrap percolation on the hypercube
Combinatorics, Probability and Computing
Theoretical Computer Science
On the Approximability of Influence in Social Networks
SIAM Journal on Discrete Mathematics
On dissemination thresholds in regular and irregular graph classes
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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
Irreversible conversion of graphs
Theoretical Computer Science
Dynamic monopolies and feedback vertex sets in hexagonal grids
Computers & Mathematics with Applications
Influential nodes in a diffusion model for social networks
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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
Discrete Applied Mathematics
Hi-index | 5.23 |
Consider the following reversible cascade on a simple directed graph G=(V,E). In round zero, a set of vertices, called the seeds, are active. In round k@?Z^+, a vertex v@?V is activated (deactivated) if at least (resp., fewer than) @f(v) of its in-neighbors are active in round k-1, where @f:V-N. An irreversible cascade is defined similarly except that active vertices cannot be deactivated. Two specific candidates for the threshold function @f are @f"m"a"j"("v")^s^t^r^i^c^t=@?(deg^-(v)+1)/2@? and @f"@r(v)=@?@r@?deg^-(v)@?, where deg^-(v) denotes the indegree of v@?V and @r@?(0,1]. An irreversible dynamic monopoly is a set of seeds that leads all vertices to activation after finitely many rounds of the irreversible cascade with @f=@f"m"a"j^s^t^r^i^c^t. A set of vertices, S, is said to be convergent if no vertex will ever change its state, from active to inactive or vice versa, once the set of active vertices equals S. This paper shows that an irreversible dynamic monopoly of size at most @?|V|/2@? can be found in polynomial (in |V|) time if G is strongly connected. Furthermore, we show that for any constant @e0, all @r@?(0,1], @f=@f"@r, p@?[(1+@e)(ln(e/@r))/n,1] and with probability 1-n^-^@W^(^1^), every convergent set of the Erdos-Renyi random graph G(n,p) has size O(@?@rn@?) or n-O(@?@rn@?). Our result on convergent sets holds for both the reversible and irreversible cascades.