Spectral Methods for Immunization of Large Networks

TL;DR

This paper introduces a spectral graph theory-based approximation algorithm for immunizing large networks against epidemics, offering improved efficiency and effectiveness over existing methods.

Contribution

It presents a novel spectral method for selecting nodes to immunize, with theoretical guarantees and superior performance on large real-world networks.

Findings

Algorithm scales well for large graphs

Outperforms state-of-the-art in epidemic containment

Provides theoretical efficiency guarantees

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 neighbor 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).