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The Structural Complexity Landscape of Finding Balance-Fair Shortest Paths (2405.18866v1)
Published 29 May 2024 in cs.DS and cs.CC
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.