Utilizing Housing Resources for Homeless Youth Through the Lens of Multiple Multi-Dimensional Knapsacks

There are over 1 million homeless youth in the U.S. each year. To reduce homelessness, U.S. Housing and Urban Development (HUD) and housing communities provide housing programs/services to homeless youth with the goal of improving their long-term situation. Housing communities are facing a difficult task of filling their housing programs, with as many youths as possible, subject to resource constraints for meeting the needs of youth. Currently, the assignment is manually done by humans working in the housing communities. In this paper, we consider the problem of assigning homeless youth to housing programs subject to resource constraints. We provide an initial abstract model for this setting and show that the problem of maximizing the total assigned youth to the programs under this model is APXhard. To solve the problem, we non-trivially formulate it as a multiple multi-dimensional knapsack problem (MMDKP), which is not known to have any approximation algorithm. We provide a first interpretable and easy-to-use greedy algorithm with logarithmic approximation ratio for solving general MMDKP. We conduct experiments on random and realistic instances of the housing assignment settings and show that our algorithm is efficient and effective in solving large instances (up to 1 million youth).