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  3. Hybrid Optimization Technique For Matrix Chain Multiplication Using Strassen's Algorithm.

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Hybrid optimization technique for matrix chain multiplication using Strassen's algorithm.

Srinivasarao Thota1, Thulasi Bikku2, Rakshitha T3

  • 1Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Amaravati, Andhra Pradesh, 522503, India.

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View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces a hybrid Matrix Chain Multiplication (MCM) method combining dynamic programming with Strassen's algorithm. The optimized MCM significantly speeds up large matrix computations, reducing execution time and memory usage.

Keywords:
Computational Complexity.Dynamic ProgrammingHybrid OptimizationMatrix Chain MultiplicationStrassen’s Algorithm

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Area of Science:

  • Computational Mathematics
  • Computer Science
  • Scientific Computing

Background:

  • Matrix Chain Multiplication (MCM) is crucial in scientific computing, graphics, and machine learning.
  • Traditional MCM uses Dynamic Programming (DP) with Memoization but suffers from O(n^3) complexity for large matrices.
  • Standard matrix multiplication is inefficient for large-scale computations.

Purpose of the Study:

  • To develop a hybrid optimization technique for Matrix Chain Multiplication.
  • To accelerate matrix multiplication by integrating Strassen's algorithm into MCM.
  • To reduce computational complexity and improve efficiency for large matrices.

Main Methods:

  • A two-phase approach: (i) optimizing matrix chain order with top-down DP and memoization, and (ii) a hybrid multiplication strategy.
  • Selective application of Strassen's algorithm (O(n^2.81)) for matrices with n ≥ 128.
  • Comparison with traditional MCM and standalone Strassen's algorithm via computational experiments.

    • Main Results:

    • The hybrid MCM method achieved significant speedups (4x-8x) compared to traditional methods.
    • Demonstrated reduction in memory consumption for large-scale applications.
    • Maintained numerical accuracy while improving performance.

    Conclusions:

    • The proposed hybrid MCM approach effectively reduces execution time and memory usage.
    • Selective integration of Strassen's algorithm enhances MCM efficiency for large matrices.
    • Opens avenues for parallel computing and GPU acceleration in matrix operations.