Matrix Chain Ordering Problem (Matrix Chain Multiplication)
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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
Space Complexity Graph
Time-Space Tradeoff
References/Citation
https://citeseerx.ist.psu.edu/viewdoc/citations?doi=10.1.1.695.2923