Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Size bounds for dynamic monopolies
Discrete Applied Mathematics
Mining the network value of customers
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Dynamic monopolies of constant size
Journal of Combinatorial Theory Series B
Local majorities, coalitions and monopolies in graphs: a review
Theoretical Computer Science
Approximating Treewidth and Pathwidth of some Classes of Perfect Graphs
ISAAC '92 Proceedings of the Third International Symposium on Algorithms and Computation
Efficient Approximation for Triangulation of Minimum Treewidth
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Maximizing the spread of influence through a social network
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Tight Lower Bounds for Certain Parameterized NP-Hard Problems
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
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
A note on maximizing the spread of influence in social networks
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Competitive influence maximization in social networks
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Influential nodes in a diffusion model for social networks
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Parameterized Complexity
Note: Combinatorial model and bounds for target set selection
Theoretical Computer Science
On the non-progressive spread of influence through social networks
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Identifying valuable customers on social networking sites for profit maximization
Expert Systems with Applications: An International Journal
Electronic Commerce Research and Applications
Interest-matching information propagation in multiple online social networks
Proceedings of the 21st ACM international conference on Information and knowledge management
Information cascade at group scale
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
| Hi-index | 0.00 |
The Target Set Selection problem proposed by Kempe, Kleinberg, and Tardos, gives a nice clean combinatorial formulation for many problems arising in economy, sociology, and medicine. Its input is a graph with vertex thresholds, the social network, and the goal is to find a subset of vertices, the target set, that "activates" a prespecified number of vertices in the graph. Activation of a vertex is defined via a so-called activation process as follows: Initially, all vertices in the target set become active. Then at each step i of the process, each vertex gets activated if the number of its active neighbors at iteration i -- 1 exceeds its threshold. The activation process is "monotone" in the sense that once a vertex is activated, it remains active for the entire process. Unsurprisingly perhaps, Target Set Selection is NPC. More surprising is the fact that both of its maximization and minimization variants turn out to be extremely hard to approximate, even for very restrictive special cases. The only known case for which the problem is known to have some sort of acceptable worst-case solution is the case where the given social network is a tree and the problem becomes polynomial-time solvable. In this paper, we attempt at extending this sparse landscape of tractable instances by considering the treewidth parameter of graphs. This parameter roughly measures the degree of tree-likeness of a given graph, e.g. the treewidth of a tree is 1, and has previously been used to tackle many classical NPhard problems in the literature. Our contribution is twofold: First, we present an algorithm for Target Set Selection running in nO(w) time, for graphs with n vertices and treewidth bounded by w. The algorithm utilizes various combinatorial properties of the problem; drifting somewhat from standard dynamic-programming algorithms for small treewidth graphs. Also, it can be adopted to much more general settings, including the case of directed graphs, weighted edges, and weighted vertices. On the other hand, we also show that it is highly unlikely to find an nO(√w) time algorithm for Target Set Selection, as this would imply a sub-exponential algorithm for all problems in SNPclass. Together with our upper bound result, this shows that the treewidth parameter determines the complexity of Target Set Selection to a large extent, and should be taken into consideration when tackling this problem in any scenario.