Student-Project-Resource Allocation: Complexity of the Symmetric Case

Ismaili, Anisse; Yamaguchi, Tomoaki; Yokoo, Makoto

doi:10.1007/978-3-030-03098-8_14

“…Rooms are indivisible, and at most one room can be allocated to each project. Ismaili et al [2018] extend this to a more general Student-Project-Resource allocation problem. Resources are still indivisible, but there is no longer a restriction imposed on the number of resources that can be allocated to each project.…”

Section: Related Workmentioning

confidence: 95%

Cutoff stability under distributional constraints with an application to summer internship matching

Aziz¹,

Baychkov²,

Bíró³

2021

Preprint

0

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We introduce a new two-sided stable matching problem that describes the summer internship matching practice of an Australian university. The model is a case between two models of Kamada and Kojima on matchings with distributional constraints. We study three solution concepts, the strong and weak stability concepts proposed by Kamada and Kojima, and a new one in between the two, called cutoff stability. Kamada and Kojima showed that a strongly stable matching may not exist in their most restricted model with disjoint regional quotas. Our first result is that checking its existence is NP-hard. We then show that a cutoff stable matching exists not just for the summer internship problem but also for the general matching model with arbitrary heredity constraints. We present an algorithm to compute a cutoff stable matching and show that it runs in polynomial time in our special case of summer internship model. However, we also show that finding a maximum size cutoff stable matching is NP-hard, but we provide a Mixed Integer Linear Program formulation for this optimisation problem.

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“…Rooms are indivisible, and at most one room can be allocated to each project. Ismaili et al [33] extend this to a more general Student-Project-Resource allocation problem. Resources are still indivisible, but there is no longer a restriction imposed on the number of resources that can be allocated to each project.…”

Section: Related Workmentioning

confidence: 99%

Cutoff stability under distributional constraints with an application to summer internship matching

Aziz

¹

,

Baychkov

²

,

Bíró

³

2022

Math. Program.

3

0

View full text Add to dashboard Cite

We introduce a new two-sided stable matching problem that describes the summer internship matching practice of an Australian university. The model is a case between two models of Kamada and Kojima on matchings with distributional constraints. We study three solution concepts, the strong and weak stability concepts proposed by Kamada and Kojima, and a new one in between the two, called cutoff stability. Kamada and Kojima showed that a strongly stable matching may not exist in their most restricted model with disjoint regional quotas. Our first result is that checking its existence is NP-hard. We then show that a cutoff stable matching exists not just for the summer internship problem but also for the general matching model with arbitrary heredity constraints. We present an algorithm to compute a cutoff stable matching and show that it runs in polynomial time in our special case of summer internship model. However, we also show that finding a maximum size cutoff stable matching is NP-hard, but we provide a Mixed Integer Linear Program formulation for this optimisation problem.

show abstract

“…Other works examine the computational complexity for finding a matching with desirable properties under distributional constraints, including [4,7,15]. A similar model was recently considered [20], but with a compact representation scheme which handles exponentially many students and induces intrinsically different computational problems.…”

Section: Related Workmentioning

confidence: 99%

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

Ismaili

2018

Preprint

Self Cite

0

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In this work, we consider a three sided student-project-resource matching-allocation problem, in which students have preferences on projects, and projects on students. While students are many-to-one matched to projects, indivisible resources are many-to-one allocated to projects whose capacities are thus endogenously determined by the sum of resources allocated to them. Traditionally, this problem is divided into two separate problems: (1) resources are allocated to projects based on some expectations (resource allocation problem), and (2) students are matched to projects based on the capacities determined in the previous problem (matching problem). Although both problems are well-understood, unless the expectations used in the first problem are correct, we obtain a suboptimal outcome. Thus, it is desirable to solve this problem as a whole without dividing it in two.Here, we show that finding a nonwasteful matching is FP NP [log]-hard, and deciding whether a stable matching exists is NP NP -complete. These results involve two new problems of independent interest: P P , shown FP NP [poly]-complete and strongly FP NP [log]-hard, and ∀∃ 4 P , shown strongly NP NP -complete.1 Without these properties, this work is still valid, though a claiming or envious pair (s, p) may not necessarily make sense. 2 For designing a strategyproof mechanism, we assume each ≻ s is private information of s, while the rest of parameters are public. Thus, X does not need to be part of the input, since it is characterized by projects' preferences.

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Student-Project-Resource Allocation: Complexity of the Symmetric Case

Cited by 6 publications

References 22 publications

Cutoff stability under distributional constraints with an application to summer internship matching

Cutoff stability under distributional constraints with an application to summer internship matching

Cutoff stability under distributional constraints with an application to summer internship matching

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

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