Maximizing Resource Allocation Likelihood with Minimum Compromise

Many scenarios where agents with preferences compete for resources can be cast as maximum matching problems on bipartite graphs. Our focus is on resource allocation problems where agents may have preferences that make them incompatible with some resources. We assume that a Principal 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 preferences within certain limits. The Principal'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 develop efficient algorithms for some variants of this budget-constrained maximization problem and establish hardness results for other variants. For the latter variants, we also develop algorithms with performance guarantees. 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.