Changeable two-sided matching for changing environment

Two-sided matching is a major matching problem for players in two groups. If a player joins or leaves a group, the matching must be calculated from scratch. In this paper, we propose a changeable two-sided matching problem for two-sided problems in changing environments where a player can join or leave groups. We also propose an algorithm, called the continuation algorithm, for this problem, which calculates matching using not only the preferences of the players of the two groups, but also the matching result of the original two-sided matching problem before changes occur. We demonstrate that, if the matching result of the original two-sided matching is stable, the result obtained by the continuation algorithm is also stable.