Citation:
Murtagh, Jack, Omer Reingold, Aaron Sidford, and Salil Vadhan. “Derandomization beyond connectivity: Undirected Laplacian systems in nearly logarithmic space.” 58th Annual IEEE Symposium on Foundations of Computer Science (FOCS `17), 2017.
 | ArXiv2017.pdf | 360 KB |
| FOCS2017.pdf | 0 bytes |
Abstract:
Version History:
ArXiv, 15 August 2017 https://arxiv.org/abs/1708.04634
FOCS, November 2017 https://ieeexplore.ieee.org/document/8104111
We give a deterministic \(\overline{O} (\log n)\)-space algorithm for approximately solving linear systems given by Laplacians of undirected graphs, and consequently also approximating hitting times, commute times, and escape probabilities for undirected graphs. Previously, such systems were known to be solvable by randomized algorithms using \(O(\log n)\) space (Doron, Le Gall, and Ta-Shma, 2017) and hence by deterministic algorithms using \( O(\log^{3/2} n)\) space (Saks and Zhou, FOCS 1995 and JCSS 1999).
Our algorithm combines ideas from time-efficient Laplacian solvers (Spielman and Teng, STOC '04; Peng and Spielman, STOC '14) with ideas used to show that Undirected S-T Connectivity is in deterministic logspace (Reingold, STOC '05 and JACM '08; Rozenman and Vadhan, RANDOM '05).