Exact Laplacian Solver (SDD Systems Solvers)
Revision as of 10:20, 15 February 2023 by Admin (talk | contribs) (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...")
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
Space Complexity graph
Pareto Decades graph
