Preserving the Basic Property of Stable Matching by Deleting a pair

TL;DR

This paper presents an algorithm that transforms a male-pessimal stable matching into a male-optimal one by deleting a pair, with theoretical analysis showing a best-case complexity of O(n^3).

Contribution

It introduces a novel method for modifying stable matchings through pair deletion to achieve optimality, supported by both sequential and parallel algorithm descriptions.

Findings

The algorithm can convert stable matchings from pessimal to optimal.

Theoretical analysis establishes a lower bound of O(n^3) for the algorithm's best case.

Parallel implementation details are provided.

Abstract

This paper describes the transition of a male-pessimal matching set to optimal when it is a man-oriented approach by deleting a pair from matching set considering the score based approach. A descriptive explanation of the proposed algorithm both in a sequential and parallel manner is given. The comparison based theoretical analysis shows that the best case of the algorithm is lower bound of n3.