The Complexity of Student-Project-Resource Matching-Allocation Problems
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In this technical note, I settle the computational complexity of nonwastefulness and stability in student-project-resource matching-allocation problems, a model that was first proposed by Yamaguchi and Yokoo (2017). I show that computing a nonwasteful matching is complete for class FP^NP[poly] and computing a stable matching is complete for class Σ_2^P. These results involve the creation of two fundamental problems: ParetoPartition, shown complete for FP^NP[poly], and ∀∃-4-Partition, shown complete for Σ_2^P. Both are number problems that are hard in the strong sense.
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