@inproceedings{0159cf0f95f447528a52c5adce03223d,
title = "Probabilistic logarithmic-space algorithms for laplacian solvers",
abstract = "A recent series of breakthroughs initiated by Spielman and Teng culminated in the construction of nearly linear time Laplacian solvers, approximating the solution of a linear system Lx = b, where L is the normalized Laplacian of an undirected graph. In this paper we study the space complexity of the problem. Surprisingly we are able to show a probabilistic, logspace algorithm solving the problem. We further extend the algorithm to other families of graphs like Eulerian graphs (and directed regular graphs) and graphs that mix in polynomial time. Our approach is to pseudo-invert the Laplacian, by first {"}peeling-off{"} the problematic kernel of the operator, and then to approximate the inverse of the remaining part by using a Taylor series. We approximate the Taylor series using a previous work and the special structure of the problem. For directed graphs we exploit in the analysis the Jordan normal form and results from matrix functions.",
keywords = "Bounded-space complexity classes, Laplacian solvers, Matrix computation, Random walks, Randomized logspace",
author = "Dean Doron and {Le Gall}, Francois and Amnon Ta-Shma",
note = "Publisher Copyright: {\textcopyright} Dean Doron, Francois Le Gall, and Amnon Ta-Shma.; 20th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2017 and the 21st International Workshop on Randomization and Computation, RANDOM 2017 ; Conference date: 16-08-2017 Through 18-08-2017",
year = "2017",
month = aug,
day = "1",
doi = "10.4230/LIPIcs.APPROX/RANDOM.2017.41",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Rolim, {Jose D. P.} and Klaus Jansen and Williamson, {David P.} and Vempala, {Santosh S.}",
booktitle = "Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 20th International Workshop, APPROX 2017 and 21st International Workshop, RANDOM 2017",
address = "Germany",
}