Matrix Chain Ordering Problem: Difference between revisions
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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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| [[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.ezproxy.canberra.edu.au/9780262046305/introduction-to-algorithms/ Space] | | [[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.ezproxy.canberra.edu.au/9780262046305/introduction-to-algorithms/ Space] | ||
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| [[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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Revision as of 08:18, 10 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
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Space Complexity Graph
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Time-Space Tradeoff
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References/Citation
https://citeseerx.ist.psu.edu/viewdoc/citations?doi=10.1.1.695.2923