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
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
On the parameterized complexity of multiple-interval graph problems
Theoretical Computer Science
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
Efficient approximation for triangulation of minimum treewidth
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Influential nodes in a diffusion model for social networks
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Parameterized Complexity
New races in parameterized algorithmics
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
The robust set problem: parameterized complexity and approximation
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Constant thresholds can make target set selection tractable
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
Large Social Networks Can Be Targeted for Viral Marketing with Small Seed Sets
ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
Proceedings of the 2nd ACM SIGPLAN workshop on Functional high-performance computing
Hi-index | 0.00 |
In this paper we study the Target Set Selection problem proposed by Kempe, Kleinberg, and Tardos; a problem which gives a nice clean combinatorial formulation for many applications 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 pre-specified 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. Our contribution is as follows: First, we present an algorithm for Target Set Selection running in n^O^(^w^) time, for graphs with n vertices and treewidth bounded by w. This algorithm 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 n^o^(^w^) time algorithm for Target Set Selection, as this would imply a sub-exponential algorithm for all problems in SNP. 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. In the last part of the paper we also deal with the ''non-monotone'' variant of Target Set Selection, and show that this problem becomes #P-hard on graphs with edge weights.