Gelling, and melting, large graphs by edge manipulation
@article{Tong2012GellingAM, title={Gelling, and melting, large graphs by edge manipulation}, author={Hanghang Tong and B. Aditya Prakash and Tina Eliassi-Rad and Michalis Faloutsos and Christos Faloutsos}, journal={Proceedings of the 21st ACM international conference on Information and knowledge management}, year={2012} }
Controlling the dissemination of an entity (e.g., meme, virus, etc) on a large graph is an interesting problem in many disciplines. Examples include epidemiology, computer security, marketing, etc. So far, previous studies have mostly focused on removing or inoculating nodes to achieve the desired outcome. We shift the problem to the level of edges and ask: which edges should we add or delete in order to speed-up or contain a dissemination? First, we propose effective and scalable algorithms to…
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References
SHOWING 1-10 OF 59 REFERENCES
On the Vulnerability of Large Graphs
- Computer Science2010 IEEE International Conference on Data Mining
- 2010
This paper gives the justification behind the choices, and shows that they agree with intuition as well as recent results in immunology, and proposes Net Shield, a fast and scalable algorithm that achieves tremendous speed savings against straightforward competitors.
The effect of network topology on the spread of epidemics
- Mathematics, Computer ScienceProceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies.
- 2005
This paper identifies topological properties of the graph that determine the persistence of epidemics and shows that if the ratio of cure to infection rates is larger than the spectral radius of thegraph, then the mean epidemic lifetime is of order log n, where n is the number of nodes.
Finding effectors in social networks
- Computer ScienceKDD
- 2010
It is shown that for arbitrary graphs the problem of selecting a set of k active nodes that best explain the observed activation state, under a given information-propagation model, is not only NP-hard to solve optimally, but also NP- hard to approximate.
Scalable influence maximization for prevalent viral marketing in large-scale social networks
- Computer ScienceKDD
- 2010
The results from extensive simulations demonstrate that the proposed algorithm is currently the best scalable solution to the influence maximization problem and significantly outperforms all other scalable heuristics to as much as 100%--260% increase in influence spread.
Virus Propagation on Time-Varying Networks: Theory and Immunization Algorithms
- Computer Science, MathematicsECML/PKDD
- 2010
This paper derives the first closed formula for the epidemic threshold of time-varying graphs under the SIS model, and shows the usefulness of the threshold by presenting efficient heuristics and evaluating the effectiveness of the methods on synthetic and real data like the MIT reality mining graphs.
Threshold conditions for arbitrary cascade models on arbitrary networks
- Computer Science2011 IEEE 11th International Conference on Data Mining
- 2011
The G2-threshold (twice generalized) theorem is shown, which nicely de-couples the effect of the topology and the virus model and has broad implications for the vulnerability of real, complex networks and numerous applications, including viral marketing, blog dynamics, influence propagation, easy answers to ‘what-if’ questions, and simplified design and evaluation of immunization policies.
Link Operations for Slowing the Spread of Disease in Complex Networks
- Computer Science
- 2011
The approach considered in this work differs from existing techniques in that it is based on optimally removing (or immunizing) individual links in the network as opposed to individual nodes.
Finding the k most vital edges with respect to minimum spanning tree
- Computer Science, MathematicsActa Informatica
- 1999
This paper presents polynomial-time randomized algorithms that produce optimal and approximate solutions to the problem of finding k edges in G whose removal will cause greatest weight increase in the minimum spanning tree of the remaining graph.
Epidemic spreading in real networks: an eigenvalue viewpoint
- Mathematics, Computer Science22nd International Symposium on Reliable Distributed Systems, 2003. Proceedings.
- 2003
A general epidemic threshold condition that applies to arbitrary graphs is proposed and it is proved that, under reasonable approximations, the epidemic threshold for a network is closely related to the largest eigenvalue of its adjacency matrix.
Subgraph sparsification and nearly optimal ultrasparsifiers
- Mathematics, Computer ScienceSTOC '10
- 2010
It is shown that for each positive integer k, every n-vertex weighted graph has an (n-1+k)-edge spectral sparsifier with relative condition number at most n/k log n, ~O(log log n) where ~O() hides lower order terms.