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arXiv · 2102.08905

The Complexity of Gerrymandering Over Graphs: Paths and Trees

Matthias Bentert·Tomohiro Koana·Rolf Niedermeier
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Abstract

Roughly speaking, gerrymandering is the systematic manipulation of the boundaries of electoral districts to make a specific (political) party win as many districts as possible. While typically studied from a geographical point of view, addressing social network structures, the investigation of gerrymandering over graphs was recently initiated by Cohen-Zemach et al. [AAMAS 2018]. Settling three open questions of Ito et al. [AAMAS 2019], we classify the computational complexity of the NP-hard problem Gerrymandering over Graphs when restricted to paths and trees. Our results, which are mostly of negative nature (that is, worst-case hardness), in particular yield two complexity dichotomies for trees. For instance, the problem is polynomial-time solvable for two parties but becomes weakly NP-hard for three. Moreover, we show that the problem remains NP-hard even when the input graph is a path.

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Matthias Bentert, Tomohiro Koana, Rolf Niedermeier. 2021-02-17. The Complexity of Gerrymandering Over Graphs: Paths and Trees. https://arxiv.org/abs/2102.08905

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