相关论文: Balanced power diagrams for redistricting

Redistricting is the problem of dividing a state into a number $k$ of regions, called districts. Voters in each district elect a representative. The primary criteria are: each district is connected, district populations are equal (or nearly…

A crucial task in the political redistricting problem is to sample redistricting plans i.e. a partitioning of the graph of census blocks into districts. We show that Recombination [DeFord-Duchin-Solomon'21]-a popular Markov chain to sample…

In the design and analysis of political redistricting maps, it is often useful to be able to sample from the space of all partitions of the graph of census blocks into connected subgraphs of equal population. There are influential Markov…

Sampling-based methods such as ReCom are widely used to audit redistricting plans for fairness, with the balanced spanning tree distribution playing a central role since it favors compact, contiguous, and population-balanced districts.…

Motivated by the problem of redistricting, we study area-preserving reconfigurations of connected subdivisions of a simple polygon. A connected subdivision of a polygon $\mathcal{R}$, called a district map, is a set of interior disjoint…

In this paper, we consider the problem of partitioning a polygon into a set of connected disjoint sub-polygons, each of which covers an area of a specific size. The work is motivated by terrain covering applications in robotics, where the…

Redistricting is the problem of partitioning a set of geographical units into a fixed number of districts, subject to a list of often-vague rules and priorities. In recent years, the use of randomized methods to sample from the vast space…

Researchers and legislators alike continue the search for methods of drawing fair districting plans. A districting plan is a partition of a state's subdivisions (e.g. counties, voting precincts, etc.). By modeling these districting plans as…

In representative democracy, a redistricting map is chosen to partition an electorate into districts which each elects a representative. A valid redistricting map must satisfy a collection of constraints such as being compact, contiguous,…

Ensemble analysis has become an important tool for quantifying gerrymandering; the main idea is to generate a large, random sample of districting plans (an "ensemble") to which any proposed plan may be compared. If a proposed plan is an…

This paper is to obtain a simple dividing-diagram of the congressional districts, where the only limit is that each district should contain the same population if possibly. In order to solve this problem, we introduce three different…

In the computational study of political redistricting, feasibility necessitates the use of a discretization of regions such as states, counties, and towns. In nearly all cases, researchers use a dual graph, whose vertices represent small…

In this paper, we propose to use the concept of local fairness for auditing and ranking redistricting plans. Given a redistricting plan, a deviating group is a population-balanced contiguous region in which a majority of individuals are of…

Redistricting is the process by which electoral district boundaries are drawn, and a common normative assumption in this process is that districts should be drawn so as to capture coherent communities of interest (COIs). While states rely…

Algorithmic and statistical approaches to congressional redistricting are becoming increasingly valuable tools in courts and redistricting commissions for quantifying gerrymandering in the United States. While there is existing literature…

Distributed resource allocation is a central task in network systems such as smart grids, water distribution networks, and urban transportation systems. When solving such problems in practice it is often important to have nonasymptotic…

A distributed, hierarchical, market based approach is introduced to solve the economic dispatch problem. The approach requires only a minimal amount of information to be shared between a central market operator and the end-users. Price…

Partisan gerrymandering poses a threat to democracy. Moreover, the complexity of the districting task may exceed human capacities. One potential solution is using computational models to automate the districting process by optimizing…

The process of drawing electoral district boundaries is known as political redistricting. Within this context, gerrymandering is the practice of drawing these boundaries such that they unfairly favor a particular political party, often…

Given a graph $G = (V,E)$ with vertex weights $w(v)$ and a desired number of parts $k$, the goal in graph partitioning problems is to partition the vertex set V into parts $V_1,\ldots,V_k$. Metrics for compactness, contiguity, and balance…