### Abstract

In this paper, we consider a student-project-resource allocation problem, in which students and indivisible resources are allocated to every project. The allocated resources determine endogenously the student capacity of a project. Traditionally, this problem is divided in two: (I) resources are allocated to projects based on expected demands (resource allocation problem), and (II) students are matched with projects based on the capacity determined in the previous problem (many-to-one 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. We start by introducing a compact representation that takes advantage of the symmetry of preferences. Then, we show that computing a nonwasteful matching is FP
^{NP}
-complete. Besides, a fair matching can be found in polynomial-time. Finally, deciding whether a stable (i.e. nonwasteful and fair) matching exists is NP
^{NP}
-complete.

Original language | English |
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Title of host publication | PRIMA 2018 |

Subtitle of host publication | Principles and Practice of Multi-Agent Systems - 21st International Conference, 2018, Proceedings |

Editors | Nir Oren, Yuko Sakurai, Itsuki Noda, Tran Cao Son, Tim Miller, Bastin Tony Savarimuthu |

Publisher | Springer Verlag |

Pages | 226-241 |

Number of pages | 16 |

ISBN (Print) | 9783030030971 |

DOIs | |

Publication status | Published - Jan 1 2018 |

Event | 21st International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2018 - Tokyo, Japan Duration: Oct 29 2018 → Nov 2 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11224 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 21st International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2018 |
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Country | Japan |

City | Tokyo |

Period | 10/29/18 → 11/2/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*PRIMA 2018: Principles and Practice of Multi-Agent Systems - 21st International Conference, 2018, Proceedings*(pp. 226-241). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11224 LNAI). Springer Verlag. https://doi.org/10.1007/978-3-030-03098-8_14

**Student-project-resource allocation : Complexity of the symmetric case.** / Ismaili, Anisse; Yamaguchi, Tomoaki; Yokoo, Makoto.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*PRIMA 2018: Principles and Practice of Multi-Agent Systems - 21st International Conference, 2018, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11224 LNAI, Springer Verlag, pp. 226-241, 21st International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2018, Tokyo, Japan, 10/29/18. https://doi.org/10.1007/978-3-030-03098-8_14

}

TY - GEN

T1 - Student-project-resource allocation

T2 - Complexity of the symmetric case

AU - Ismaili, Anisse

AU - Yamaguchi, Tomoaki

AU - Yokoo, Makoto

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this paper, we consider a student-project-resource allocation problem, in which students and indivisible resources are allocated to every project. The allocated resources determine endogenously the student capacity of a project. Traditionally, this problem is divided in two: (I) resources are allocated to projects based on expected demands (resource allocation problem), and (II) students are matched with projects based on the capacity determined in the previous problem (many-to-one 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. We start by introducing a compact representation that takes advantage of the symmetry of preferences. Then, we show that computing a nonwasteful matching is FP NP -complete. Besides, a fair matching can be found in polynomial-time. Finally, deciding whether a stable (i.e. nonwasteful and fair) matching exists is NP NP -complete.

AB - In this paper, we consider a student-project-resource allocation problem, in which students and indivisible resources are allocated to every project. The allocated resources determine endogenously the student capacity of a project. Traditionally, this problem is divided in two: (I) resources are allocated to projects based on expected demands (resource allocation problem), and (II) students are matched with projects based on the capacity determined in the previous problem (many-to-one 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. We start by introducing a compact representation that takes advantage of the symmetry of preferences. Then, we show that computing a nonwasteful matching is FP NP -complete. Besides, a fair matching can be found in polynomial-time. Finally, deciding whether a stable (i.e. nonwasteful and fair) matching exists is NP NP -complete.

UR - http://www.scopus.com/inward/record.url?scp=85056486332&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056486332&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-03098-8_14

DO - 10.1007/978-3-030-03098-8_14

M3 - Conference contribution

AN - SCOPUS:85056486332

SN - 9783030030971

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 226

EP - 241

BT - PRIMA 2018

A2 - Oren, Nir

A2 - Sakurai, Yuko

A2 - Noda, Itsuki

A2 - Cao Son, Tran

A2 - Miller, Tim

A2 - Savarimuthu, Bastin Tony

PB - Springer Verlag

ER -