Nonpartisan Political Redistricting by Computer

Hess, Sidney W.; Weaver, James B.; Siegfeldt, H. J.; Whelan, JJ; Zitlau, P. A.

doi:10.1287/opre.13.6.998

Cited by 264 publications

(180 citation statements)

References 11 publications

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“…Traditionally, population equality and compactness are the main and widely accepted criteria for political districting [1,5]. In general, population equality can be taken into account by a constraint which forces the population of each district between fixed upper and/or lower bounds [7]. Let p be the average district population and α a given real in [0,1].…”

Section: Introductionmentioning

confidence: 99%

Polynomial algorithms for partitioning a tree into single‐center subtrees to minimize flat service costs

et al. 2007

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This paper deals with the following graph partitioning problem: given a graph with n nodes, p of which are prescribed to be centers (the remaining nodes are called units), the goal is to find a partition of the set of nodes into connected components containing only one center each, so as to minimize the total assignment cost of units to centers. This problem is known to be NP-hard in general graphs, and it is shown here to remain such even if the assignment cost is monotone and the graph is bipartite. Therefore, we specialize on tree graphs to derive polynomial time algorithms. For this class of graphs we provide several reformulations of the problem as integer linear programs. Moreover, we develop a dynamic programming algorithm, whose recursion is based on solving sequences of minimum weight closure problems, that solves the problem on trees in O(n 2 p).

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Section: Introductionmentioning

confidence: 99%

Polynomial algorithms for partitioning a tree into single‐center subtrees to minimize flat service costs

et al. 2007

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“…Although, after an extensive literature search, no model is specifically designed for MSW collection, several mixed integer programming (MIP) models are available for other types of districting problems. For instance, Hess et al 7 proposed an MIP model, probably the first, for voting districting problems. The model partitions a region into a prespecified number of districts that maximizes the sum of the compactness values for all subregions.…”

Section: Discussionmentioning

confidence: 99%

“…Most subregion districting models have been constructed for developing voting districts or sales territories. [7][8][9][10][11][12] Among these studies,…”

Section: Introductionmentioning

confidence: 99%

Subregion Districting Analysis for Municipal Solid Waste Collection Privatization

Lin

Kao

2008

Journal of the Air & Waste Management Association

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Privatization of municipal solid waste (MSW) collection can improve service quality and reduce cost. To reduce the risk of an incapable company serving an entire collection area and to establish a competitive market, a large collection area should be divided into two or more subregions, with each subregion served by a different company. The MSW subregion districting is generally done manually, based on the planner's intuition. Major drawbacks of a manual approach include the creation of a districting plan with poor road network integrity for which it is difficult to design an efficient collection route. The other drawbacks are difficulty in finding the optimal districting plan and the lack of a way to consistently measure the differences among subregions to avoid unfair competition. To determine an MSW collection subregion districting plan, this study presents a mixed-integer optimization model that incorporates factors such as compactness, road network integrity, collection cost, and regional proximity. Two cases are presented to demonstrate the applicability of the proposed model. In both cases, districting plans with good road network integrity and regional proximity have been generated successfully.

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“…For example, Harris proposed rectangle method in solving the districting problems [2]. In 1965, Hess presented a linear programming method in optimizing the electoral districting [3]. Kaiser then focused on the population equalization by using the mathematical model to solve the districting problems [4].…”

Section: Related Studiesmentioning

confidence: 99%

Improving Electoral Districting through Geographic Information Systems

Hor¹,

Peng²

2015

Proceedings of the 2015 International Conference on Computer Science and Intelligent Communication

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Abstract-In this paper, we present an approach that can solve the electoral districting problems by integrating the technologies of dynamics programming, computational geometry as well as the geographic information systems. A quantitative measurement to evaluate the shape of the districting results is also presented. We have applied these methods to Changhua County in Taiwan and obtained more than hundred thousands of feasible solutions.

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Nonpartisan Political Redistricting by Computer

Cited by 264 publications

References 11 publications

Polynomial algorithms for partitioning a tree into single‐center subtrees to minimize flat service costs

Polynomial algorithms for partitioning a tree into single‐center subtrees to minimize flat service costs

Subregion Districting Analysis for Municipal Solid Waste Collection Privatization

Improving Electoral Districting through Geographic Information Systems

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