Dynamic effective resistances and approximate schur complement on separable graphs
Goranci G, Henzinger MH, 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.
Download (ext.)
Conference Paper
| Published
| English
Scopus indexed
Author
Goranci, Gramoz;
Henzinger, MonikaISTA
;
Peng, Pan
![](https://research-explorer.ista.ac.at/images/icon_orcid.png)
Series Title
LIPIcs
Abstract
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.
Publishing Year
Date Published
2018-08-14
Proceedings Title
26th Annual European Symposium on Algorithms
Volume
112
Article Number
40
Conference
ESA: Annual European Symposium on Algorithms
Conference Location
Helsinki, Finland
Conference Date
2018-08-20 – 2018-08-22
ISBN
ISSN
IST-REx-ID
Cite this
Goranci G, Henzinger MH, Peng P. Dynamic effective resistances and approximate schur complement on separable graphs. In: 26th Annual European Symposium on Algorithms. Vol 112. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:10.4230/LIPICS.ESA.2018.40
Goranci, G., Henzinger, M. H., & Peng, P. (2018). Dynamic effective resistances and approximate schur complement on separable graphs. In 26th Annual European Symposium on Algorithms (Vol. 112). Helsinki, Finland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.ESA.2018.40
Goranci, Gramoz, Monika H Henzinger, and Pan Peng. “Dynamic Effective Resistances and Approximate Schur Complement on Separable Graphs.” In 26th Annual European Symposium on Algorithms, Vol. 112. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPICS.ESA.2018.40.
G. Goranci, M. H. Henzinger, and P. Peng, “Dynamic effective resistances and approximate schur complement on separable graphs,” in 26th Annual European Symposium on Algorithms, Helsinki, Finland, 2018, vol. 112.
Goranci G, Henzinger MH, 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, et al. “Dynamic Effective Resistances and Approximate Schur Complement on Separable Graphs.” 26th Annual European Symposium on Algorithms, vol. 112, 40, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:10.4230/LIPICS.ESA.2018.40.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]
Link(s) to Main File(s)
Access Level
![Open access file OA](https://research-explorer.ista.ac.at/images/access_open.png)
Export
Marked PublicationsOpen Data ISTA Research Explorer
Sources
arXiv 1802.09111