A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
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
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)
Decycling Cartesian Products of Two Cycles
SIAM Journal on Discrete Mathematics
On the submodularity of influence in social networks
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Theoretical Computer Science
Influential nodes in a diffusion model for social networks
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Note: Combinatorial model and bounds for target set selection
Theoretical Computer Science
Dynamic monopolies with randomized starting configuration
Theoretical Computer Science
Dynamic monopolies and feedback vertex sets in hexagonal grids
Computers & Mathematics with Applications
Stable sets of threshold-based cascades on the erdős-rényi random graphs
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Discrete Applied Mathematics
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
Hi-index | 0.00 |
Consider the following coloring process in a simple directed graph G(V,E) with positive indegrees. Initially, a set S of vertices are white. Thereafter, a black vertex is colored white whenever the majority of its in-neighbors are white. The coloring process ends when no additional vertices can be colored white. If all vertices end up white, we call S an irreversible dynamic monopoly (or dynamo for short). We derive upper bounds of 0.7732|V| and 0.727|V| on the minimum sizes of irreversible dynamos depending on whether the majority is strict or simple. When G is an undirected connected graph without isolated vertices, upper bounds of ⌈|V|/2 ⌉ and $\lfloor |V|/2 \rfloor$ are given on the minimum sizes of irreversible dynamos depending on whether the majority is strict or simple. Let ε0 be any constant. We also show that, unless $\text{NP}\subseteq \text{TIME}(n^{O(\ln \ln n)}),$ no polynomial-time, ((1/2−ε)ln |V|)-approximation algorithms exist for finding a minimum irreversible dynamo.