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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
A Modern Approach to Electoral Delimitation using the Qua...
Sahil Kale, Gautam Khaire, Jay Patankar, Pujashree Vidap · 2024-02-15 · via cs.DS updates on arXiv.org

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.