相关论文: Balanced power diagrams for redistricting

The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…

Large-scale integration of distributed energy resources into residential distribution feeders necessitates careful control of their operation through power flow analysis. While the knowledge of the distribution system model is crucial for…

We describe a new approach for dealing with the following central problem in the self-organization of a geometric sensor network: Given a polygonal region R, and a large, dense set of sensor nodes that are scattered uniformly at random in…

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…

This study develops a statistical model that integrates economic agglomeration theory and power-law distributions of city sizes to project future population distribution on 1-km grid cells. We focus on Japan -- a country at the forefront of…

As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…

Given a set of disjoint simple polygons $\sigma_1, \ldots, \sigma_n$, of total complexity $N$, consider a convexification process that repeatedly replaces a polygon by its convex hull, and any two (by now convex) polygons that intersect by…

This study introduces a new districting approach using the US Postal Service network to measure community connectivity. We combine Topological Data Analysis with Markov Chain Monte Carlo methods to assess district boundaries' impact on…

In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…

Spectrum resources management of growing demands is a challenging problem and Cognitive Radio (CR) known to be capable of improving the spectrum utilization. Recently, Power Spectral Density (PSD) map is defined to enable the CR to reuse…

This paper considers a distributed convex optimization problem with inequality constraints over time-varying unbalanced digraphs, where the cost function is a sum of local objectives, and each node of the graph only knows its local…

Given a set of sites in a simple polygon, a geodesic Voronoi diagram of the sites partitions the polygon into regions based on distances to sites under the geodesic metric. We present algorithms for computing the geodesic nearest-point,…

In this article, we advance divide-and-conquer strategies for solving the community detection problem in networks. We propose two algorithms which perform clustering on a number of small subgraphs and finally patches the results into a…

The paper addresses large-scale, convex optimization problems that need to be solved in a distributed way by agents communicating according to a random time-varying graph. Specifically, the goal of the network is to minimize the sum of…

We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can be dissected by axis-parallel cuts and…

This paper considers the low-observability state estimation problem in power distribution networks and develops a decentralized state estimation algorithm leveraging the matrix completion methodology. Matrix completion has been shown to be…

In this work, a heterogeneous set of wireless devices sharing a common access point collaborates to perform a set of tasks. Using the Map-Reduce distributed computing framework, the tasks are optimally distributed amongst the nodes with the…

We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…

This paper deals with energy management in a district where multiple buildings can communicate over a time-varying network and aim at optimizing the use of shared resources like storage systems. We focus on building cooling, and propose an…

Interpolating between measures supported by polygonal or polyhedral domains is a problem that has been recently addressed by the semi-discrete optimal transport framework. Within this framework, one of the domains is discretized with a set…