Authors
Jan van den Brand, Yu Gao, Arun Jambulapati, Yin Tat Lee, Yang P Liu, Richard Peng, Aaron Sidford
Publication date
2021/12/1
Journal
arXiv preprint arXiv:2112.00722
Description
We make several advances broadly related to the maintenance of electrical flows in weighted graphs undergoing dynamic resistance updates, including: 1. More efficient dynamic spectral vertex sparsification, achieved by faster length estimation of random walks in weighted graphs using Morris counters [Morris 1978, Nelson-Yu 2020]. 2. A direct reduction from detecting edges with large energy in dynamic electric flows to dynamic spectral vertex sparsifiers. 3. A procedure for turning algorithms for estimating a sequence of vectors under updates from an oblivious adversary to one that tolerates adaptive adversaries via the Gaussian-mechanism from differential privacy. Combining these pieces with modifications to prior robust interior point frameworks gives an algorithm that on graphs with edges computes a mincost flow with edge costs and capacities in in time . In prior and independent work, [Axiotis-M\k{a}dry-Vladu FOCS 2021] also obtained an improved algorithm for sparse mincost flows on capacitated graphs. Our algorithm implies a time maxflow algorithm, improving over the time maxflow algorithm of [Gao-Liu-Peng FOCS 2021].
Scholar articles
J Brand, Y Gao, A Jambulapati, YT Lee, YP Liu, R Peng… - arXiv preprint arXiv:2112.00722, 2021