Matrix Chain Ordering Problem: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Matrix Chain Ordering Problem (Matrix Chain Multiplication)}} == Description == Matrix chain multiplication (or Matrix Chain Ordering Problem; MCOP) is an optimization problem. Given a sequence of matrices, the goal is to find the most efficient way to multiply these matrices. == Related Problems == Subproblem: Approximate MCOP, Matrix Chain Scheduling Problem Related: Matrix Chain Scheduling Problem, Approximate MCSP == Parameters...") |
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== Related Problems == | == Related Problems == | ||
Subproblem: [[Approximate MCOP | Subproblem: [[Approximate MCOP]] | ||
Related: [[Matrix Chain Scheduling Problem]], [[Approximate MCSP]] | Related: [[Matrix Chain Scheduling Problem]], [[Approximate MCSP]] | ||
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== Parameters == | == Parameters == | ||
$n$: number of matrices | |||
== Table of Algorithms == | == Table of Algorithms == | ||
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| [[Brute Force (Matrix Chain Ordering Problem Matrix Chain Multiplication)|Brute Force]] || 1940 || O ({4}^n) || $O(n)$ || Exact || Deterministic || | | [[Brute Force (Matrix Chain Ordering Problem Matrix Chain Multiplication)|Brute Force]] || 1940 || $O({4}^n)$ || $O(n)$ || Exact || Deterministic || | ||
|- | |- | ||
| [[Dynamic Programming Algorithm (S. S. Godbole) (Matrix Chain Ordering Problem Matrix Chain Multiplication)|Dynamic Programming Algorithm (S. S. Godbole)]] || 1953 || $O(n^{3})$ || $O(n^{2})$ || Exact || Deterministic || | | [[Dynamic Programming Algorithm (S. S. Godbole) (Matrix Chain Ordering Problem Matrix Chain Multiplication)|Dynamic Programming Algorithm (S. S. Godbole)]] || 1953 || $O(n^{3})$ || $O(n^{2})$ || Exact || Deterministic || [http://mitpress.mit.edu/9780262046305/introduction-to-algorithms/ Space] | ||
|- | |- | ||
| [[T. C. Hu ; M. T. Shing (Matrix Chain Ordering Problem Matrix Chain Multiplication)|T. C. Hu ; M. T. Shing]] || 1982 || $O( | | [[T. C. Hu ; M. T. Shing (Matrix Chain Ordering Problem Matrix Chain Multiplication)|T. C. Hu ; M. T. Shing]] || 1982 || $O(n \log n)$ || $O(n)$ || Exact || Deterministic || [https://doi.org/10.1137/0211028 Time] | ||
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|} | |} | ||
== Time Complexity | == Time Complexity Graph == | ||
[[File:Matrix Chain Multiplication - Matrix Chain Ordering Problem - Time.png|1000px]] | [[File:Matrix Chain Multiplication - Matrix Chain Ordering Problem - Time.png|1000px]] | ||
== References/Citation == | == References/Citation == | ||
https://citeseerx.ist.psu.edu/viewdoc/citations?doi=10.1.1.695.2923 | https://citeseerx.ist.psu.edu/viewdoc/citations?doi=10.1.1.695.2923 | ||
Latest revision as of 09:04, 28 April 2023
Description
Matrix chain multiplication (or Matrix Chain Ordering Problem; MCOP) is an optimization problem. Given a sequence of matrices, the goal is to find the most efficient way to multiply these matrices.
Related Problems
Subproblem: Approximate MCOP
Related: Matrix Chain Scheduling Problem, Approximate MCSP
Parameters
$n$: number of matrices
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Brute Force | 1940 | $O({4}^n)$ | $O(n)$ | Exact | Deterministic | |
| Dynamic Programming Algorithm (S. S. Godbole) | 1953 | $O(n^{3})$ | $O(n^{2})$ | Exact | Deterministic | Space |
| T. C. Hu ; M. T. Shing | 1982 | $O(n \log n)$ | $O(n)$ | Exact | Deterministic | Time |
Time Complexity Graph
References/Citation
https://citeseerx.ist.psu.edu/viewdoc/citations?doi=10.1.1.695.2923