{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/multiple-node-immunisation-for-preventing","title":"Multiple Node Immunisation for Preventing Epidemics on Networks by Exact Multiobjective Optimisation of Cost and Shield-Value","arxiv_id":"2010.06488","date":"2020-10-13","proceeding":null,"authors":["Michael Emmerich","Joost Nibbeling","Marios Kefalas","Aske Plaat"],"abstract":"The general problem in this paper is vertex (node) subset selection with the goal to contain an infection that spreads in a network. Instead of selecting the single most important node, this paper deals with the problem of selecting multiple nodes for removal. As compared to previous work on multiple-node selection, the trade-off between cost and benefit is considered. The benefit is measured in terms of increasing the epidemic threshold which is a measure of how difficult it is for an infection to spread in a network. The cost is measured in terms of the number and size of nodes to be removed or controlled. Already in its single-objective instance with a fixed number of $k$ nodes to be removed, the multiple vertex immunisation problems have been proven to be NP-hard. Several heuristics have been developed to approximate the problem. In this work, we compare meta-heuristic techniques with exact methods on the Shield-value, which is a sub-modular proxy for the maximal eigenvalue and used in the current state-of-the-art greedy node-removal strategies. We generalise it to the multi-objective case and replace the greedy algorithm by a quadratic program (QP), which then can be solved with exact QP solvers. The main contribution of this paper is the insight that, if time permits, exact and problem-specific methods approximation should be used, which are often far better than Pareto front approximations obtained by general meta-heuristics. Based on these, it will be more effective to develop strategies for controlling real-world networks when the goal is to prevent or contain epidemic outbreaks. This paper is supported by ready to use Python implementation of the optimization methods and datasets.","url_abs":"https://arxiv.org/abs/2010.06488v1","url_pdf":"https://arxiv.org/pdf/2010.06488v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"multiple-node-immunisation-for-preventing","repo_url":"https://github.com/joostnibbeling/node-immunisation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}