Spectral Methods for Immunization of Large Networks

Muhammad Ahmad, Juvaria Tariq, Mudassir Shabbir, Imdadullah Khan

Abstract


Given a network of nodes, minimizing the spread of a contagion using a limited budget is a well-studied problem with applications in network security, viral marketing, social networks, and public health. In real graphs, virus may infect a node which in turn infects its neighbour nodes and this may trigger an epidemic in the whole graph. The goal thus is to select the best k nodes (budget constraint) that are immunized (vaccinated, screened, filtered) so as the remaining graph is less prone to the epidemic. It is known that the problem is, in all practical models, computationally intractable even for moderate sized graphs. In this paper we employ ideas from spectral graph theory to define relevance and importance of nodes. Using novel graph theoretic techniques, we then design an efficient approximation algorithm to immunize the graph. Theoretical guarantees on the running time of our algorithm show that it is more efficient than any other known solution in the literature. We test the performance of our algorithm on several real world graphs. Experiments show that our algorithm scales well for large graphs and outperforms state of the art algorithms both in quality (containment of epidemic) and efficiency (runtime and space complexity).

Keywords


graph immunization; eigendrop; closed walks

Full Text:

PDF


DOI: http://dx.doi.org/10.3127/ajis.v21i0.1563

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Creative Commons License
ISSN: Online: 1326-2238 Hard copy: 1449-8618
This work is licensed under a Creative Commons Attribution-NonCommercial Licence. Uses the Open Journal Systems. Web design by TomW.