Derandomization Beyond Connectivity: Undirected Laplacian Systems in Nearly Logarithmic Space

Jack Murtagh, Omer Reingold, Aaron Sidford, Salil Vadhan
2017 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)  
We give a deterministicÕ(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
more » ... bines 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).
doi:10.1109/focs.2017.79 dblp:conf/focs/MurtaghRSV17 fatcat:hw3sxqd5wvgnljea3yrdqb54oy