Pairing optimization via statistics: Algebraic structure in pairing problems and its application to performance enhancement

TL;DR

This paper reveals algebraic structures in pairing problems, transforming the compatibility data to enhance pairing optimization, leading to significantly better total compatibility results applicable to fields like wireless communications.

Contribution

It introduces a novel algebraic approach to transform and optimize pairing problems, improving upon previous methods by exploiting underlying mathematical properties.

Findings

Transformed compatibility data reduces variance in individual compatibilities.

Heuristic pairing on the transformed problem yields higher total compatibility.

Applicable to practical fields like wireless communications beyond 5G.

Abstract

Fully pairing all elements of a set while attempting to maximize the total benefit is a combinatorically difficult problem. Such pairing problems naturally appear in various situations in science, technology, economics, and other fields. In our previous study, we proposed an efficient method to infer the underlying compatibilities among the entities, under the constraint that only the total compatibility is observable. Furthermore, by transforming the pairing problem into a traveling salesman problem with a multi-layer architecture, a pairing optimization algorithm was successfully demonstrated to derive a high-total-compatibility pairing. However, there is substantial room for further performance enhancement by further exploiting the underlying mathematical properties. In this study, we prove the existence of algebraic structures in the pairing problem. We transform the initially estimated compatibility information into an equivalent form where the variance of the individual compatibilities is minimized. We then demonstrate that the total compatibility obtained when using the heuristic pairing algorithm on the transformed problem is significantly higher compared to the previous method. With this improved perspective on the pairing problem using fundamental mathematical properties, we can contribute to practical applications such as wireless communications beyond 5G, where efficient pairing is of critical importance.