The covering of a graph with (possibly disjoint) connected subgraphs is fundamental problem in theory. In this paper, we study version to cover graph's vertices by subject lower and upper weight bounds, propose column generation approach dynamically generate feasible promising subgraphs. Our focus on the solution pricing which turns out be variant NP-hard Maximum Weight Connected Subgraph Probl...

In this paper, we present an empirical evaluation of a metaheuristic approach to a commercial districting problem. The problem consists of partitioning a given set of basic units into p districts so as minimize a measure of territory dispersion. Additional constraints include territory connectivity and balancing with respect to several criteria. To obtain feasible solutions to this NP-hard prob...

Sectorization is concerned with dividing a large territory into smaller areas, also known as sectors. This process usually simplifies complex problem, leading to easier solution approaches solving the resulting subproblems. Sectors are built several criteria in mind, such equilibrium, compactness, contiguity, and desirability, which vary applications. appears different contexts: sales design, p...

We introduce a graph-theoretic dissolution model that applies to a number of redistribution scenarios such as gerrymandering in political districting or work balancing in an online situation. The central aspect of our model is the deletion of certain vertices and the redistribution of their loads to neighboring vertices in a perfectly balanced way. We investigate how the underlying graph struct...

Territory design can be defined as the problem which is focused on grouping small geographical areas into larger geographic clusters. These clusters may be referenced as territories. On this paper we develop the case where two or more attributes must be considered in order to setup an optimal territory design. We developed a new strategy which is based on a hybrid-mixed integer programming meth...

We apply persistent homology, the dominant tool from field of topological data analysis, to study electoral redistricting. begin by combining geographic and a districting plan produce persistence diagram. Then, see beyond particular understand possibilities afforded choices made in redistricting, we build methods visualize analyze large ensembles alternative plans. Our detailed case studies use...

Segmentation is one popular method for geospatial data mining. We propose efficient and effective sequential-scan algorithms for higher-order Voronoi diagram districting. We extend the distance transform algorithm to include complex primitives (point, line, and area), Minkowski metrics, different weights and obstacles for higher-order Voronoi diagrams. The algorithm implementation is explained ...

Electoral districting and gerrymandering are problems as old at the United States itself. In this project, by employing opinion dynamics on some social networks and using their community structure, we seek to model elections in a two party political system like the USA and simulate the phenomenon that gerrymanders attempt to use to their advantage electorates within different districts or spher...

While single-member districting (smd) is the most common form of representation in the U.S., apportionment schemes at the state and local level often make use of multimember districts (Klain 1955; Jewell 1971), the polar type of which is, of course, the at-Iarge election; •'̂ and in one state (New York) weighted voting is the most common of the various systems in use for county government.^ In t...