Computational Complexity of Envy-free and Exchange-stable Seat Arrangement Problems on Grid Graphs
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916563732398080 |
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| author | Kawase, Sota Miyazaki, Shuichi |
| author_facet | Kawase, Sota Miyazaki, Shuichi |
| contents | The Seat Arrangement Problem is a problem of finding a desirable seat arrangement for given preferences of agents and a seat graph that represents a configuration of seats. In this paper, we consider decision problems of determining if an envy-free arrangement exists and an exchange-stable arrangement exists, when a seat graph is an $\ell \times m$ grid graph. When $\ell=1$, the seat graph is a path of length $m$ and both problems have been known to be NP-complete. In this paper, we extend it and show that both problems are NP-complete for any integer $\ell \geq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10719 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computational Complexity of Envy-free and Exchange-stable Seat Arrangement Problems on Grid Graphs Kawase, Sota Miyazaki, Shuichi Computer Science and Game Theory Computational Complexity Data Structures and Algorithms The Seat Arrangement Problem is a problem of finding a desirable seat arrangement for given preferences of agents and a seat graph that represents a configuration of seats. In this paper, we consider decision problems of determining if an envy-free arrangement exists and an exchange-stable arrangement exists, when a seat graph is an $\ell \times m$ grid graph. When $\ell=1$, the seat graph is a path of length $m$ and both problems have been known to be NP-complete. In this paper, we extend it and show that both problems are NP-complete for any integer $\ell \geq 2$. |
| title | Computational Complexity of Envy-free and Exchange-stable Seat Arrangement Problems on Grid Graphs |
| topic | Computer Science and Game Theory Computational Complexity Data Structures and Algorithms |
| url | https://arxiv.org/abs/2411.10719 |