Exact Laplacian Solver: Difference between revisions
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== Time Complexity | == Time Complexity Graph == | ||
[[File:SDD Systems Solvers - Exact Laplacian Solver - Time.png|1000px]] | [[File:SDD Systems Solvers - Exact Laplacian Solver - Time.png|1000px]] | ||
== Space Complexity | == Space Complexity Graph == | ||
[[File:SDD Systems Solvers - Exact Laplacian Solver - Space.png|1000px]] | [[File:SDD Systems Solvers - Exact Laplacian Solver - Space.png|1000px]] | ||
== Pareto | == Pareto Frontier Improvements Graph == | ||
[[File:SDD Systems Solvers - Exact Laplacian Solver - Pareto Frontier.png|1000px]] | [[File:SDD Systems Solvers - Exact Laplacian Solver - Pareto Frontier.png|1000px]] | ||
Revision as of 13:04, 15 February 2023
Description
This problem refers to solving equations of the form $Lx = b$ where $L$ is a Laplacian of a graph. In other words, this is solving equations of the form $Ax = b$ for a SDD matrix $A$.
This variation of the problem requires an exact solution with no error.
Related Problems
Related: Inexact Laplacian Solver
Parameters
n: dimension of matrix
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Briggs; Henson; McCormick | 2000 | $O(n^{1.{2}5} loglogn)$ | Exact | Deterministic | Time | |
| Gaussian Elimination | -150 | $O(n^{3})$ | $O(n^{2})$ | Exact | Deterministic | |
| Naive Implementation | 1940 | $O(n!)$ | $O(n^{2})$ | Exact | Deterministic |
Time Complexity Graph
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Space Complexity Graph
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Pareto Frontier Improvements Graph
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