Algorithms for gerrymandering over graphs

Takehiro Ito, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto

Research output: Contribution to journalArticlepeer-review

Abstract

We initiate the systematic algorithmic study for gerrymandering over graphs that was recently introduced by Cohen-Zemach, Lewenberg and Rosenschein. Namely, we study a strategic procedure for a political districting designer to draw electoral district boundaries so that a particular target candidate can win in an election. We focus on the existence of such a strategy under the plurality voting rule, and give interesting contrasts which classify easy and hard instances with respect to polynomial-time solvability. For example, we prove that the problem for trees is strongly NP-complete (thus unlikely to have a pseudo-polynomial-time algorithm), but has a pseudo-polynomial-time algorithm when the number of candidates is constant. Another example is to prove that the problem for complete graphs is NP-complete when the number of electoral districts is two, while is solvable in polynomial time when it is more than two.

Original languageEnglish
Pages (from-to)30-45
Number of pages16
JournalTheoretical Computer Science
Volume868
DOIs
Publication statusPublished - 2021 May 8

Keywords

  • Computational social choice
  • Gerrymandering
  • Graph algorithms

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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