Why Districting Becomes NP-hard
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908619161731072 |
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| author | Jost, Niklas Escobedo, Adolfo Kirchheim, Alice |
| author_facet | Jost, Niklas Escobedo, Adolfo Kirchheim, Alice |
| contents | This paper investigates why and when the edge-based districting problem becomes computationally intractable. The overall problem is represented as an exact mathematical programming formulation consisting of an objective function and several constraint groups, each enforcing a well-known districting criterion such as balance, contiguity, or compactness. While districting is known to be NP-hard in general, we study what happens when specific constraint groups are relaxed or removed. The results identify precise boundaries between tractable subproblems (in P) and intractable ones (NP-hard). The paper also discusses implications on node-based analogs of the featured districting problems, and it considers alternative notions of certain criteria in its analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25614 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Why Districting Becomes NP-hard Jost, Niklas Escobedo, Adolfo Kirchheim, Alice Discrete Mathematics This paper investigates why and when the edge-based districting problem becomes computationally intractable. The overall problem is represented as an exact mathematical programming formulation consisting of an objective function and several constraint groups, each enforcing a well-known districting criterion such as balance, contiguity, or compactness. While districting is known to be NP-hard in general, we study what happens when specific constraint groups are relaxed or removed. The results identify precise boundaries between tractable subproblems (in P) and intractable ones (NP-hard). The paper also discusses implications on node-based analogs of the featured districting problems, and it considers alternative notions of certain criteria in its analysis. |
| title | Why Districting Becomes NP-hard |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/2510.25614 |