Exact Laplacian Solver: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Exact Laplacian Solver (SDD Systems Solvers)}} == 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 == <pre>n: dimension of matrix</pre> == Table of Algor...") |
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== Parameters == | == Parameters == | ||
$n$: dimension of matrix | |||
== Table of Algorithms == | == Table of Algorithms == | ||
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| [[Briggs; Henson; McCormick ( SDD Systems Solvers)|Briggs; Henson; McCormick]] || 2000 || $O(n^{1.{2}5} | | [[Briggs; Henson; McCormick ( SDD Systems Solvers)|Briggs; Henson; McCormick]] || 2000 || $O(n^{1.{2}5} \log \log n)$ || || Exact || Deterministic || [http://www.math.ust.hk/~mamu/courses/531/tutorial_with_corrections.pdf Time] | ||
|- | |- | ||
| [[Gaussian Elimination (Exact Laplacian Solver SDD Systems Solvers)|Gaussian Elimination]] || -150 || $O(n^{3})$ || $O(n^{2})$ || Exact || Deterministic || | | [[Gaussian Elimination (Exact Laplacian Solver SDD Systems Solvers)|Gaussian Elimination]] || -150 || $O(n^{3})$ || $O(n^{2})$ || Exact || Deterministic || | ||
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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]] | ||
Latest revision as of 09:07, 28 April 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 | $O(n^{1.{2}5} \log \log n)$ | 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
