Size bounds for dynamic monopolies
Discrete Applied Mathematics
Approximation algorithms
Mining the network value of customers
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
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
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
On the submodularity of influence in social networks
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On the approximability of influence in social networks
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Theoretical Computer Science
An exact almost optimal algorithm for target set selection in social networks
Proceedings of the 10th ACM conference on Electronic commerce
Influential nodes in a diffusion model for social networks
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Bounding the number of tolerable faults in majority-based systems
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
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
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
Generalized degeneracy, dynamic monopolies and maximum degenerate subgraphs
Discrete Applied Mathematics
Hi-index | 5.23 |
The adoption of everyday decisions in public affairs, fashion, movie-going, and consumer behavior is now thoroughly believed to migrate in a population through an influential network. The same diffusion process when being imitated by intention is called viral marketing. This process can be modeled by a (directed) graph G=(V,E) with a threshold t(v) for every vertex v@?V, where v becomes active once at least t(v) of its (in-)neighbors are already active. A Perfect Target Set is a set of vertices whose activation will eventually activate the entire graph, and the Perfect Target Set Selection Problem (PTSS) asks for the minimum such initial set. It is known (Chen (2008) [6]) that PTSS is hard to approximate, even for some special cases such as bounded-degree graphs, or majority thresholds. We propose a combinatorial model for this dynamic activation process, and use it to represent PTSS and its variants by linear integer programs. This allows one to use standard integer programming solvers for solving small-size PTSS instances. We also show combinatorial lower and upper bounds on the size of the minimum Perfect Target Set. Our upper bound implies that there are always Perfect Target Sets of size at most |V|/2 and 2|V|/3 under majority and strict majority thresholds, respectively, both in directed and undirected graphs. This improves the bounds of 0.727|V| and 0.7732|V| found recently by Chang and Lyuu (2010) [5] for majority and strict majority thresholds in directed graphs, and matches their bound under majority thresholds in undirected graphs. Furthermore, our proof is much simpler, and we observe that some of these bounds are tight. One interesting and perhaps surprising implication of our lower bound for undirected graphs, is that it is easy to get a constant factor approximation for PTSS for ''relatively balanced'' graphs (e.g., bounded-degree graphs, nearly regular graphs) with a ''more than majority'' threshold (that is, t(v)=@q@?deg(v), for every v@?V and some constant @q1/2), whereas no polylogarithmic approximation exists for ''more than majority'' graphs.