conference paper published yes Gramoz Goranci author Monika H Henzinger author 540c9bbd-f2de-11ec-812d-d04a5be856300000-0002-5008-6530 Pan Peng author ESA: Annual European Symposium on Algorithms 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 Informatik2018Helsinki, Finland eng 1868-8969 9783959770811 1802.0911110.4230/LIPICS.ESA.2018.40 112 yes 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> 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>. 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. 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> G. Goranci, M. Henzinger, P. Peng, in:, 26th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. 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. 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>. 118282022-08-12T08:26:42Z2024-11-06T12:16:31Z