Optimal partisan districting on planar geographies

We show that optimal partisan districting in the plane with geographical constraints is an NP-complete problem

The political districting problem: A survey

Computer scientists and social scientists consider the political districting problem from different viewpoints. This paper gives an overview of both strands of the literature on districting in which the connections and the differences between the two approaches are highlighted

A Modern Approach to Electoral Delimitation using the Quadtree Data Structure

The boundaries of electoral constituencies for assembly and parliamentary seats are drafted using a process referred to as delimitation, which ensures fair and equal representation of all citizens. The current delimitation exercise suffers from a number of drawbacks viz. inefficiency, gerrymandering and an uneven seat-to-population ratio, owing to existing legal and constitutional dictates. The existing methods allocate seats to every state but remain silent about their actual shape and location within the state. The main purpose of this research is to study and analyse the performance of existing delimitation algorithms and further propose a potential solution, along with its merits, that involves using a computational model based on the quadtree data structure to automate the districting process by optimizing objective population criteria. The paper presents an approach to electoral delimitation using the quadtree data structure, which is used to partition a two-dimensional geographical space by recursively subdividing it into four quadrants or regions on the basis of population as a parameter value associated with the node. The quadtree makes use of a quadrant schema of the geographical space for representing constituencies, which not only keeps count of the allocated constituencies but also holds their location-specific information. The performance of the proposed algorithm is analysed and evaluated against existing techniques and proves to be an efficient solution in terms of algorithmic complexity and boundary visualisation to the process of political districting.Comment: 7 pages, 6 figures, Accepted in 1st International Conference on Cognitive Computing and Engineering Education (ICCCEE), Pune, India, 202

A MATHEMATICAL MODEL FOR UNIFORM DISTRIBUTION OF VOTERS PER CONSTITUENCIES

This paper presents two different approaches on the basis how to generate constituencies. The first one is based on cluster analysis by means of which approach can get compact constituencies having an approximately equal number of voters. An optimal number of constituencies can be obtained by using this method. The second approach is based on partitioning the country into several areas with respect to territorial integrity of bigger administrative units. The units obtained in this way will represent constituencies which do not necessarily have to have an approximately equal number of voters. Each constituency is associated with a number of representatives that is proportional to its number of voters, so the problem is reduced to the integer approximation problem. Finally, these two approaches are combined and applied on the Republic of Croatia

Optimal partisan districting on planar geographies

We show that optimal partisan districting and majority securing districting in the plane with geographical constraints are NP-complete problems. We provide a polynomial time algorithm for determining an optimal partisan districting for a simplified version of the problem. In addition, we give possible explanations for why finding an optimal partisan districting for real-life problems cannot be guaranteed

Redefinition of the Greek electoral districts through the application of a region-building algorithm

The main purpose of this paper is the formulation of a methodological approach for the definition of homogenous spatial clusters, taking into account both geographical and descriptive characteristics. The proposed methodology, is substantiated by SPiRAL (SPatial Integration and Redistricting ALgorithm), a constrained-based spatial clustering algorithm, whose successive steps focus on the analysis of the characteristics of the areas being integrated, the designation of the spatial clusters and the validity of a joining criterion. We applied the methodological approach and used SPiRAL to solve a realistic electoral redistricting problem. Namely, the redefinition of the electoral districts of the Prefecture of Lakonia in Greece. The results demonstrate an improved layout of the study area’s electoral map as far as the problem’s criteria and constraints are concerned (adjacency, population and size), justifying in this respect the perspectives and potential of our approach in the analysis and confrontation of similar problems

DISTRICT DESIGN AND ROUTE PLANNING FOR CUSTOMER-RELATED FIELD OPERATIONS OF NATURAL GAS DISTRIBUTION SYSTEMS: A CASE STUDY

Dünya enerji ihtiyacının yaklaşık % 24'ü doğalgazdan karşılanmaktadır. Bir şehirde, doğal gaz dağıtım sistemi, yapım, işletme, iç tesisat ve müşteri hizmetleri olmak üzere birbirine bağlı dört ana süreçten oluşur. Bu çalışmada, dağıtım sisteminin müşteri ile doğrudan ilişkili olan müşteri hizmetleri süreçleri ele alınmıştır. Bölgesel ayrım, rota planlaması ve mobil ekip iş yükü tahsisi gibi müşteri hizmetleri süreçleri için matematiksel modeller önerilmiş ve Konya'nın yetkili doğal gaz dağıtım şirketi olan Gaznet A.Ş.'de uygulanmıştır. Önerilen modellerin performansı, mobil ekip sayısı ve iş yükü miktarı açısından mevcut sistemle karşılaştırılmıştır. Deneysel çalışmalar, önerilen sistemin mobil ekip sayısının mevcut sistemden % 37 daha düşük olduğunu göstermektedir