Matrix-Chain Multiplication Using Greedy and Divide-Conquer approach
Raghav Lakhotia, Sanjeev Kumar, Rishabh Sood, Harmeet Singh, Javaid Nabi "Matrix-Chain Multiplication Using Greedy and Divide-Conquer approach". International Journal of Computer Trends and Technology (IJCTT) V23(2):65-72, May 2015. ISSN:2231-2803. www.ijcttjournal.org. Published by Seventh Sense Research Group.
Matrix Chain Multiplication is a famous application of optimization problem and is used widely in signal processing and network industry for routing. The crux of the solution lies in minimizing the cost or minimizing the number of arithmetic operations required to multiply out the matrices. A top-down dynamic approach is a well-known solution for this problem which helps to determine the minimal cost required to perform the required multiplication of the matrices. The dynamic solution bears time complexity of the order ? .The authors in this paper present a greedy approach to find the optimal computation order of matrix chain multiplication. This approach provides the minimum cost required to compute the required result in a runtime of the order ? as compared to the dynamic approach runtime of ? . Although the end result i.e. the matrix obtained after the chain multiplication provided by theapproaches, the proposed approach and the dynamic approach is the same.
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Matrix Chain Multiplication, Dynamic Approach, Greedy Approach.