Abstract: A 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 Laplacian of an undirected graph.
In this talk we study the space complexity of the problem. We show a probabilistic, logspace algorithm solving the problem. We further extend the algorithm to other families of graphs like Eulerian graphs and graphs that mix in polynomial time.
We also shortly discuss complexity-theoretic motivations for studying linear-algebraic problems in small space, and relations to local algorithms.