Artificial Intelligence

   

The Complexity of Student-Project-Resource Matching-Allocation Problems

Authors: Anisse Ismaili

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 \cite{pc2017}. I show that computing a nonwasteful matching is complete for class $\text{FP}^{\text{NP}}[\text{poly}]$ and computing a stable matching is complete for class $\Sigma_2^P$. These results involve the creation of two fundamental problems: \textsc{ParetoPartition}, shown complete for $\text{FP}^{\text{NP}}[\text{poly}]$, and \textsc{$\forall\exists$-4-Partition}, shown complete for $\Sigma_2^P$. Both are number problems that are hard in the strong sense.

Comments: 6 Pages.

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Submission history

[v1] 2018-08-27 07:02:11

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