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Space Hardness of Solving Structured Linear Systems

Author Xuangui Huang

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Xuangui Huang
  • Northeastern University, Boston, MA, USA


The author thanks Emanuele Viola for helpful discussions, and anonymous reviewers for comments.

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Xuangui Huang. Space Hardness of Solving Structured Linear Systems. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 56:1-56:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


Space-efficient Laplacian solvers are closely related to derandomization of space-bound randomized computations. We show that if the probabilistic logarithmic-space solver or the deterministic nearly logarithmic-space solver for undirected Laplacian matrices can be extended to solve slightly larger subclasses of linear systems, then they can be used to solve all linear systems with similar space complexity. Previously Kyng and Zhang [Rasmus Kyng and Peng Zhang, 2017] proved such results in the time complexity setting using reductions between approximate solvers. We prove that their reductions can be implemented using constant-depth, polynomial-size threshold circuits.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • linear system solver
  • logarithmic space
  • threshold circuit


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