安定マッチング問題に関する最近の話題

Abstract

安定マッチング問題とは, 男女の集合と, 各人の異性に対する希望リストが与えられたとき, 「安定性」と呼ばれる性質を満たす男女間のマッチングを求める問題である.本問題は, 研修医の病院配属や生徒の学校への配属, 大学における学生の研究室配属等, 応用の広い問題である.本講演では, 本問題の紹介を行うと共に, 関連するいくつかの問題に対する最近の話題を, 著者の研究グループが得た成果を中心に紹介する.

In the stable matching problem, we are given a set of men and women, and each person's preference list that orders members of the opposite gender. Our task is to find a matching between men and women that satisfies the "stability" condition. This problem has wide variety of applications in real-world, such as assigning medical students to hospitals, primary school students to secondary schools, and graduate students to supervisors. In this presentation, we introduce the problem and show some elementary properties of the problem. We also show some of recent results on this problem, which are mainly obtained by the authors.