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The Cartographer
The Structural Complexity Landscape of Finding Balance-Fair Shortest Paths
May 29, 2024 Β· Declared Dead Β· π arXiv.org
"No code URL or promise found in abstract"
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Authors
Matthias Bentert, Leon Kellerhals, Rolf Niedermeier
arXiv ID
2405.18866
Category
cs.DS: Data Structures & Algorithms
Cross-listed
cs.CC
Citations
0
Venue
arXiv.org
Last Checked
5 months ago
Abstract
We study the parameterized complexity of finding shortest s-t-paths with an additional fairness requirement. The task is to compute a shortest path in a vertex-colored graph where each color appears (roughly) equally often in the solution. We provide a complete picture of the parameterized complexity landscape of the problem with respect to structural parameters by showing a tetrachotomy including polynomial kernels, fixed-parameter tractability, XP-time algorithms (and W[1]-hardness), and para-NP-hardness.
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