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DOI: 10.4230/LIPIcs.FORC.2024.7

Drawing Competitive Districts in Redistricting

Authors: Gabriel Chuang, Oussama Hanguir, and Clifford Stein

Published in: LIPIcs, Volume 295, 5th Symposium on Foundations of Responsible Computing (FORC 2024)

Abstract

In the process of redistricting, one important metric is the number of competitive districts, that is, districts where both parties have a reasonable chance of winning a majority of votes. Competitive districts are important for achieving proportionality, responsiveness, and other desirable qualities; some states even directly list competitiveness in their legally-codified districting requirements. In this work, we discuss the problem of drawing plans with at least a fixed number of competitive districts. In addition to the standard, "vote-band" measure of competitivenesss (i.e., how close was the last election?), we propose a measure that explicitly considers "swing voters" - the segment of the population that may choose to vote either way, or not vote at all, in a given election. We present two main, contrasting results. First, from a computational complexity perspective, we show that the task of drawing plans with competitive districts is NP-hard, even on very natural instances where the districting task itself is easy (e.g., small rectangular grids of population-balanced cells). Second, however, we show that a simple hill-climbing procedure can in practice find districtings on real states in which all the districts are competitive. We present the results of the latter on the precinct-level graphs of the U.S. states of North Carolina and Arizona, and discuss trade-offs between competitiveness and other desirable qualities.

Cite as

Gabriel Chuang, Oussama Hanguir, and Clifford Stein. Drawing Competitive Districts in Redistricting. In 5th Symposium on Foundations of Responsible Computing (FORC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 295, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chuang_et_al:LIPIcs.FORC.2024.7,
  author =	{Chuang, Gabriel and Hanguir, Oussama and Stein, Clifford},
  title =	{{Drawing Competitive Districts in Redistricting}},
  booktitle =	{5th Symposium on Foundations of Responsible Computing (FORC 2024)},
  pages =	{7:1--7:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-319-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{295},
  editor =	{Rothblum, Guy N.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2024.7},
  URN =		{urn:nbn:de:0030-drops-200902},
  doi =		{10.4230/LIPIcs.FORC.2024.7},
  annote =	{Keywords: Redistricting, Computational Complexity, Algorithms}
}

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APPROX

DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.12

Matching Drivers to Riders: A Two-Stage Robust Approach

Authors: Omar El Housni, Vineet Goyal, Oussama Hanguir, and Clifford Stein

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract

Matching demand (riders) to supply (drivers) efficiently is a fundamental problem for ride-hailing platforms who need to match the riders (almost) as soon as the request arrives with only partial knowledge about future ride requests. A myopic approach that computes an optimal matching for current requests ignoring future uncertainty can be highly sub-optimal. In this paper, we consider a two-stage robust optimization framework for this matching problem where future demand uncertainty is modeled using a set of demand scenarios (specified explicitly or implicitly). The goal is to match the current request to drivers (in the first stage) so that the cost of first stage matching and the worst-case cost over all scenarios for the second stage matching is minimized. We show that this two-stage robust matching is NP-hard under both explicit and implicit models of uncertainty. We present constant approximation algorithms for both models of uncertainty under different settings and show they improve significantly over standard greedy approaches.

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Omar El Housni, Vineet Goyal, Oussama Hanguir, and Clifford Stein. Matching Drivers to Riders: A Two-Stage Robust Approach. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{housni_et_al:LIPIcs.APPROX/RANDOM.2021.12,
  author =	{Housni, Omar El and Goyal, Vineet and Hanguir, Oussama and Stein, Clifford},
  title =	{{Matching Drivers to Riders: A Two-Stage Robust Approach}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{12:1--12:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.12},
  URN =		{urn:nbn:de:0030-drops-147054},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.12},
  annote =	{Keywords: matching, robust optimization, approximation algorithms}
}

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Documents authored by Hanguir, Oussama

Drawing Competitive Districts in Redistricting

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Matching Drivers to Riders: A Two-Stage Robust Approach

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