Dynamic effective resistances and approximate schur complement on separable graphs LIPIcs Goranci, Gramoz Henzinger, Monika H ; https://orcid.org/0000-0002-5008-6530 Peng, Pan 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. We 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. We 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. Schloss Dagstuhl - Leibniz-Zentrum für Informatik 2018 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text http://purl.org/coar/resource_type/c_5794 https://research-explorer.ista.ac.at/record/11828 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> eng info:eu-repo/semantics/altIdentifier/doi/10.4230/LIPICS.ESA.2018.40 info:eu-repo/semantics/altIdentifier/issn/1868-8969 info:eu-repo/semantics/altIdentifier/isbn/9783959770811 info:eu-repo/semantics/altIdentifier/arxiv/1802.09111 info:eu-repo/semantics/openAccess