Maria Predari, Lukas Berner, Robert Kooij, Henning Meyerhenke
{"title":"Greedy optimization of resistance-based graph robustness with global and local edge insertions","authors":"Maria Predari, Lukas Berner, Robert Kooij, Henning Meyerhenke","doi":"10.1007/s13278-023-01137-1","DOIUrl":null,"url":null,"abstract":"Abstract The total effective resistance, also called the Kirchhoff index, provides a robustness measure for a graph G . We consider two optimization problems of adding k new edges to G such that the resulting graph has minimal total effective resistance (i.e., is most robust)—one where the new edges can be anywhere in the graph and one where the new edges need to be incident to a specified focus node. The total effective resistance and effective resistances between nodes can be computed using the pseudoinverse of the graph Laplacian. The pseudoinverse may be computed explicitly via pseudoinversion, yet this takes cubic time in practice and quadratic space. We instead exploit combinatorial and algebraic connections to speed up gain computations in an established generic greedy heuristic. Moreover, we leverage existing randomized techniques to boost the performance of our approaches by introducing a sub-sampling step. Our different graph- and matrix-based approaches are indeed significantly faster than the state-of-the-art greedy algorithm, while their quality remains reasonably high and is often quite close. Our experiments show that we can now process larger graphs for which the application of the state-of-the-art greedy approach was impractical before.","PeriodicalId":21842,"journal":{"name":"Social Network Analysis and Mining","volume":"55 9 1","pages":"0"},"PeriodicalIF":2.3000,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Social Network Analysis and Mining","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13278-023-01137-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract The total effective resistance, also called the Kirchhoff index, provides a robustness measure for a graph G . We consider two optimization problems of adding k new edges to G such that the resulting graph has minimal total effective resistance (i.e., is most robust)—one where the new edges can be anywhere in the graph and one where the new edges need to be incident to a specified focus node. The total effective resistance and effective resistances between nodes can be computed using the pseudoinverse of the graph Laplacian. The pseudoinverse may be computed explicitly via pseudoinversion, yet this takes cubic time in practice and quadratic space. We instead exploit combinatorial and algebraic connections to speed up gain computations in an established generic greedy heuristic. Moreover, we leverage existing randomized techniques to boost the performance of our approaches by introducing a sub-sampling step. Our different graph- and matrix-based approaches are indeed significantly faster than the state-of-the-art greedy algorithm, while their quality remains reasonably high and is often quite close. Our experiments show that we can now process larger graphs for which the application of the state-of-the-art greedy approach was impractical before.
期刊介绍:
Social Network Analysis and Mining (SNAM) is a multidisciplinary journal serving researchers and practitioners in academia and industry. It is the main venue for a wide range of researchers and readers from computer science, network science, social sciences, mathematical sciences, medical and biological sciences, financial, management and political sciences. We solicit experimental and theoretical work on social network analysis and mining using a wide range of techniques from social sciences, mathematics, statistics, physics, network science and computer science. The main areas covered by SNAM include: (1) data mining advances on the discovery and analysis of communities, personalization for solitary activities (e.g. search) and social activities (e.g. discovery of potential friends), the analysis of user behavior in open forums (e.g. conventional sites, blogs and forums) and in commercial platforms (e.g. e-auctions), and the associated security and privacy-preservation challenges; (2) social network modeling, construction of scalable and customizable social network infrastructure, identification and discovery of complex, dynamics, growth, and evolution patterns using machine learning and data mining approaches or multi-agent based simulation; (3) social network analysis and mining for open source intelligence and homeland security. Papers should elaborate on data mining and machine learning or related methods, issues associated to data preparation and pattern interpretation, both for conventional data (usage logs, query logs, document collections) and for multimedia data (pictures and their annotations, multi-channel usage data). Topics include but are not limited to: Applications of social network in business engineering, scientific and medical domains, homeland security, terrorism and criminology, fraud detection, public sector, politics, and case studies.