{"_id":"11828","publication_status":"published","abstract":[{"text":"We consider the problem of dynamically maintaining (approximate) all-pairs effective resistances in separable graphs, which are those that admit an n^{c}-separator theorem for some c<1. We give a fully dynamic algorithm that maintains (1+epsilon)-approximations of the all-pairs effective resistances of an n-vertex graph G undergoing edge insertions and deletions with O~(sqrt{n}/epsilon^2) worst-case update time and O~(sqrt{n}/epsilon^2) worst-case query time, if G is guaranteed to be sqrt{n}-separable (i.e., it is taken from a class satisfying a sqrt{n}-separator theorem) and its separator can be computed in O~(n) time. Our algorithm is built upon a dynamic algorithm for maintaining approximate Schur complement that approximately preserves pairwise effective resistances among a set of terminals for separable graphs, which might be of independent interest.\r\nWe complement our result by proving that for any two fixed vertices s and t, no incremental or decremental algorithm can maintain the s-t effective resistance for sqrt{n}-separable graphs with worst-case update time O(n^{1/2-delta}) and query time O(n^{1-delta}) for any delta>0, unless the Online Matrix Vector Multiplication (OMv) conjecture is false.\r\nWe further show that for general graphs, no incremental or decremental algorithm can maintain the s-t effective resistance problem with worst-case update time O(n^{1-delta}) and query-time O(n^{2-delta}) for any delta >0, unless the OMv conjecture is false.","lang":"eng"}],"month":"08","date_published":"2018-08-14T00:00:00Z","extern":"1","article_number":"40","oa_version":"Published Version","publication":"26th Annual European Symposium on Algorithms","title":"Dynamic effective resistances and approximate schur complement on separable graphs","arxiv":1,"corr_author":"1","citation":{"short":"G. Goranci, M. Henzinger, P. Peng, in:, 26th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018.","ieee":"G. Goranci, M. Henzinger, and P. Peng, “Dynamic effective resistances and approximate schur complement on separable graphs,” in <i>26th Annual European Symposium on Algorithms</i>, Helsinki, Finland, 2018, vol. 112.","apa":"Goranci, G., Henzinger, M., &#38; Peng, P. (2018). Dynamic effective resistances and approximate schur complement on separable graphs. In <i>26th Annual European Symposium on Algorithms</i> (Vol. 112). Helsinki, Finland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPICS.ESA.2018.40\">https://doi.org/10.4230/LIPICS.ESA.2018.40</a>","ama":"Goranci G, Henzinger M, Peng P. Dynamic effective resistances and approximate schur complement on separable graphs. In: <i>26th Annual European Symposium on Algorithms</i>. Vol 112. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:<a href=\"https://doi.org/10.4230/LIPICS.ESA.2018.40\">10.4230/LIPICS.ESA.2018.40</a>","ista":"Goranci G, Henzinger M, Peng P. 2018. Dynamic effective resistances and approximate schur complement on separable graphs. 26th Annual European Symposium on Algorithms. ESA: Annual European Symposium on Algorithms, LIPIcs, vol. 112, 40.","chicago":"Goranci, Gramoz, Monika Henzinger, and Pan Peng. “Dynamic Effective Resistances and Approximate Schur Complement on Separable Graphs.” In <i>26th Annual European Symposium on Algorithms</i>, Vol. 112. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. <a href=\"https://doi.org/10.4230/LIPICS.ESA.2018.40\">https://doi.org/10.4230/LIPICS.ESA.2018.40</a>.","mla":"Goranci, Gramoz, et al. “Dynamic Effective Resistances and Approximate Schur Complement on Separable Graphs.” <i>26th Annual European Symposium on Algorithms</i>, vol. 112, 40, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:<a href=\"https://doi.org/10.4230/LIPICS.ESA.2018.40\">10.4230/LIPICS.ESA.2018.40</a>."},"quality_controlled":"1","publication_identifier":{"issn":["1868-8969"],"isbn":["9783959770811"]},"intvolume":"       112","article_processing_charge":"No","volume":112,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.4230/LIPIcs.ESA.2018.40"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Goranci, Gramoz","first_name":"Gramoz","last_name":"Goranci"},{"full_name":"Henzinger, Monika H","last_name":"Henzinger","first_name":"Monika H","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"},{"first_name":"Pan","last_name":"Peng","full_name":"Peng, Pan"}],"date_updated":"2024-11-06T12:16:31Z","day":"14","external_id":{"arxiv":["1802.09111"]},"status":"public","oa":1,"conference":{"location":"Helsinki, Finland","start_date":"2018-08-20","name":"ESA: Annual European Symposium on Algorithms","end_date":"2018-08-22"},"year":"2018","scopus_import":"1","doi":"10.4230/LIPICS.ESA.2018.40","type":"conference","language":[{"iso":"eng"}],"alternative_title":["LIPIcs"],"date_created":"2022-08-12T08:26:42Z"}