New Challenges in Matching with Constraints.

In recent years, several new challenges have been observed in the application of matching theory. One important realization is that real-life matching markets are often subject to various constraints. These practical problems impose different forms of constraints on the markets which makes them different from the classical matching model. Consequently, we cannot employ classical mechanisms in these new challenges and a stable outcome, the standard solution in matching theory, is no longer guaranteed to exist. For example, one of the most pressing issues nowadays is how to allocate refugees to hosts in a safe and timely manner. The main objective of this research is to design algorithms for these new emerging problems that satisfy desirable properties while taking agents' preferences into account. Given the number of agents that participate in the market is huge, we also consider the computational efficiency to be of central importance. We are interested in designing algorithms that yield reasonable outcomes efficiently. If an algorithm could not be implemented in polynomial-time, then it is not regarded as a suitable solution.