论文标题
在线2阶段稳定匹配
Online 2-stage Stable Matching
论文作者
论文摘要
我们专注于一个在线的2阶段问题，这是在以下情况下进行的：考虑一个应分配给大学的系统。在第一轮中，一些学生申请了一些学生，必须计算出第一个（稳定的）匹配$ m_1 $。但是，一些学生可能会决定离开系统（更改计划，去外国大学或不在系统中的某些机构）。然后，在第二轮（在这些删除之后）中，我们将计算第二个（最终）稳定的匹配$ m_2 $。由于不希望更改作业，目标是最大程度地减少两个稳定匹配$ m_1 $和$ m_2 $之间的离婚/修改数量。那么，我们应该如何选择$ m_1 $和$ m_2 $？我们表明，有一个{\ it Optival Online}算法可以解决此问题。特别是，由于具有优势属性，我们表明我们可以最佳地计算$ M_1 $，而无需知道会离开系统的学生。我们将结果推广到输入（学生，开放位置）中的其他一些可能的修改。 我们还解决了更多阶段的情况，这表明在有3个阶段后，就无法为被考虑的问题实现竞争性（在线）算法。
We focus on an online 2-stage problem, motivated by the following situation: consider a system where students shall be assigned to universities. There is a first round where some students apply, and a first (stable) matching $M_1$ has to be computed. However, some students may decide to leave the system (change their plan, go to a foreign university, or to some institution not in the system). Then, in a second round (after these deletions), we shall compute a second (final) stable matching $M_2$. As it is undesirable to change assignments, the goal is to minimize the number of divorces/modifications between the two stable matchings $M_1$ and $M_2$. Then, how should we choose $M_1$ and $M_2$? We show that there is an {\it optimal online} algorithm to solve this problem. In particular, thanks to a dominance property, we show that we can optimally compute $M_1$ without knowing the students that will leave the system. We generalize the result to some other possible modifications in the input (students, open positions). We also tackle the case of more stages, showing that no competitive (online) algorithm can be achieved for the considered problem as soon as there are 3 stages.
