Orbit-finite linear programming
An infinite set is orbit-finite if, up to permutations of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of linear inequalities. As our principal contribution we provide a decision procedure for che...
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| Veröffentlicht in: | Journal of the ACM 2024-11 |
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| creator | Ghosh, Arka Hofman, Piotr Lasota, S awomir |
| description | An infinite set is orbit-finite if, up to permutations of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of linear inequalities. As our principal contribution we provide a decision procedure for checking if such a system has a real solution, and for computing the minimal/maximal value of a linear objective function over the solution set. We also show undecidability of these problems in case when only integer solutions are considered. Therefore orbit-finite linear programming is decidable, while orbit-finite integer linear programming is not. |
| doi_str_mv | 10.1145/3703909 |
| format | Article |
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| subjects | Integer programming Linear programming Theory of computation |
| title | Orbit-finite linear programming |
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