Bipartite Matching for Repeated Allocation Problems

Many applications involving the allocation of resources or tasks can be modeled as matching problems in bipartite graphs. In many of these applications, allocation is performed multiple times. An example is the allocation of classrooms to course instructors, which is done every semester. To improve their chances of being assigned, instructors may relax some of their restrictions. Another example is course and classroom assignments made for weekly workdays. In this case, however, the assignment is made multiple times at once (once for each workday of the week). Finally, in task assignment problems where resources are reusable, each resource can be assigned multiple times. We describe algorithmic solutions to some of these problems and demonstrate their effectiveness in applications such as car teleoperation, desk sharing, and classroom assignment. Finally, we discuss several directions and ideas for extending our work and solving other relevant problems.