A logical calculus of the ideas immanent in nervous activity
Neurocomputing: foundations of research
Randomized algorithms
Size bounds for dynamic monopolies
Discrete Applied 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
Euro-Par '98 Proceedings of the 4th International Euro-Par Conference on Parallel Processing
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
The power of small coalitions in graphs
Discrete Applied Mathematics
Graph Immunity Against Local Influence
Graph Immunity Against Local Influence
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating average parameters of graphs
Random Structures & Algorithms
Note: Combinatorial model and bounds for target set selection
Theoretical Computer Science
Dynamic monopolies with randomized starting configuration
Theoretical Computer Science
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
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
Bounding the sizes of dynamic monopolies and convergent sets for threshold-based cascades
Theoretical Computer Science
Active learning for networked data based on non-progressive diffusion model
Proceedings of the 7th ACM international conference on Web search and data mining
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We model a network in which messages spread by a simple directed graph G=(V,E) and a function @a:V-N mapping each v@?V to a positive integer less than or equal to the indegree of v. The graph G represents the individuals in the network and the communication channels between them. An individual v@?V will be convinced of a message when at least @a(v) of its in-neighbors are convinced. Suppose we are to convince a message to the individuals by first convincing a subset of individuals, called the seeds, and then let the message spread. We study the minimum number min-seed (G,@a) of seeds needed to convince all individuals at the end. In particular, we prove a lower bound on min-seed (G,@a) and the NP-completeness of computing min-seed (G,@a). We also analyze the special case, called the strict-majority scenario, where each individual is convinced of a message when more than half of its in-neighbors are convinced. For the strict-majority scenario, we prove three results. First, we show that with high probability over the Erdos-Renyi random graphs G(n,p), @W(min{n,1/p}) seeds are needed to convince all individuals at the end. Second, if G=(V,E) is undirected, then a set of s uniformly random samples from V convinces no more than an expected s(2|E|+2|V|)|V| individuals at the end. Third, in a digraph G=(V,E) with a positive minimum indegree, one can find in polynomial (in |V|) time a set of at most (23/27)|V| seeds convincing all individuals.