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Pairing Optimization via Statistics: Algebraic Structure in Pairing Problems and Its Application to Performance

Naoki Fujita1, André Röhm1, Takatomo Mihana1

  • 1Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.

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This study reveals algebraic structures in pairing problems, transforming compatibility data to minimize variance. This novel approach significantly enhances pairing optimization for applications like wireless communications.

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Area of Science:

  • Combinatorial Optimization
  • Applied Mathematics
  • Wireless Communications

Background:

  • Pairing problems, aiming to maximize total benefit, are combinatorically complex.
  • Previous work established methods for inferring compatibilities and optimizing pairings using a Traveling Salesman Problem transformation.
  • Further performance enhancements were sought by exploring underlying mathematical properties.

Purpose of the Study:

  • To prove the existence of algebraic structures within pairing problems.
  • To develop a novel transformation of compatibility information to minimize individual compatibility variance.
  • To significantly improve pairing optimization algorithms.

Main Methods:

  • Proving the existence of algebraic structures in pairing problems.
  • Transforming compatibility data to a form minimizing individual variance.
  • Applying a heuristic pairing algorithm to the transformed problem.

Main Results:

  • Demonstrated significant increases in total compatibility compared to previous methods.
  • Showcased the effectiveness of leveraging algebraic structures for optimization.
  • Validated the improved performance of the heuristic algorithm on the transformed problem.

Conclusions:

  • The study introduces a new mathematical perspective on pairing problems.
  • Findings offer enhanced solutions for critical applications like wireless communications beyond 5G.
  • Implications extend to maximum weighted matching and algorithms on fully connected graphs.