Matrix Chain Ordering Problem: Difference between revisions
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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]] | ||
== Space Complexity | == Space Complexity Graph == | ||
[[File:Matrix Chain Multiplication - Matrix Chain Ordering Problem - Space.png|1000px]] | [[File:Matrix Chain Multiplication - Matrix Chain Ordering Problem - Space.png|1000px]] | ||
== Pareto | == Pareto Frontier Improvements Graph == | ||
[[File:Matrix Chain Multiplication - Matrix Chain Ordering Problem - Pareto Frontier.png|1000px]] | [[File:Matrix Chain Multiplication - Matrix Chain Ordering Problem - Pareto Frontier.png|1000px]] | ||
Revision as of 13:03, 15 February 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, Matrix Chain Scheduling Problem
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 | |
| T. C. Hu ; M. T. Shing | 1982 | $O(nlogn)$ | $O(n)$ | Exact | Deterministic | Time |
Time Complexity Graph
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Space Complexity Graph
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Pareto Frontier Improvements Graph
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References/Citation
https://citeseerx.ist.psu.edu/viewdoc/citations?doi=10.1.1.695.2923