Resource Allocation to Agents with Restrictions: Maximizing Likelihood with Minimum Compromise
This addresses resource allocation challenges for agents with constraints, but it is incremental as it builds on existing maximum matching frameworks.
The paper tackles the problem of advising agents with restrictions on how to relax constraints to maximize their probability of being matched to resources under a budget, establishing hardness results and algorithmic solutions. It experimentally evaluates these methods on synthetic and real-world datasets, such as vacation activities and classrooms.
Many scenarios where agents with restrictions compete for resources can be cast as maximum matching problems on bipartite graphs. Our focus is on resource allocation problems where agents may have restrictions that make them incompatible with some resources. We assume that a Principle chooses a maximum matching randomly so that each agent is matched to a resource with some probability. Agents would like to improve their chances of being matched by modifying their restrictions within certain limits. The Principle's goal is to advise an unsatisfied agent to relax its restrictions so that the total cost of relaxation is within a budget (chosen by the agent) and the increase in the probability of being assigned a resource is maximized. We establish hardness results for some variants of this budget-constrained maximization problem and present algorithmic results for other variants. We experimentally evaluate our methods on synthetic datasets as well as on two novel real-world datasets: a vacation activities dataset and a classrooms dataset.