相关论文: On the Complexity of Sampling Redistricting Plans

We study the computational complexity of the map redistricting problem (gerrymandering). Mathematically, the electoral district designer (gerrymanderer) attempts to partition a weighted graph into $k$ connected components (districts) such…

Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges…

Sampling from learned high-dimensional distributions is a foundational computational problem. We introduce U-turn chains: Markov chains obtained by iterating short forward-backward steps of a diffusion model, in which each step proposes a…

We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…

Recently, an increasing number of researchers, especially in the realm of political redistricting, have proposed sampling-based techniques to generate a subset of plans from the vast space of districting plans. These techniques have been…

Practical image segmentation tasks concern images which must be reconstructed from noisy, distorted, and/or incomplete observations. A recent approach for solving such tasks is to perform this reconstruction jointly with the segmentation,…

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,…

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…

Identifying important nodes in complex networks is essential in theoretical and applied fields. A small number of such nodes have deterministic power to decide information spreading, so it is of importance to find a set of nodes that…

We develop effective methods for constructing an ensemble of district plans via independent sampling from a reasonable probability distribution on the space of graph partitions. We compare the performance of our algorithms to that of…

The accuracy of the recombination estimation method of Padhukasahasram et al. 2006 can be improved by including additional informative summary statistics in the rejection scheme and by simulating datasets under a fixed segregating sites…

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…

This paper gives a new algorithm for sampling tree-weighted partitions of a large class of planar graphs. Formally, the tree-weighted distribution on $k$-partitions of a graph weights $k$-partitions proportional to the product of the number…

Reconstructing weighted networks from partial information is necessary in many important circumstances, e.g. for a correct estimation of systemic risk. It has been shown that, in order to achieve an accurate reconstruction, it is crucial to…

This work presents generalized low-rank signal decompositions with the aid of switching techniques and adaptive algorithms, which do not require eigen-decompositions, for space-time adaptive processing. A generalized scheme is proposed to…

Several approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a supervised learning problem, have been proposed recently. Finding good policies…

Sampling techniques such as Respondent-Driven Sampling (RDS) are widely used in epidemiology to sample "hidden" populations, such that properties of the network can be deduced from the sample. We consider how similar techniques can be…

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…

Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…

Matrix completion algorithms fill missing entries in a large matrix given a subset of observed samples. However, how to best pre-select informative matrix entries given a sampling budget is largely unaddressed. In this paper, we propose a…