Enhancing Bucket Sort Efficiency: A Combinatorial Approach to Algorithm Optimization

Abstract: The efficiency of sorting algorithms is critical to numerous computational processes, including data management, search operations, and real-time applications. Among these algorithms, Bucket Sort is notable for its linear-time performance when data is uniformly distributed over a defined range. However, its efficiency suffers significantly with non-uniform data distributions, resulting in unbalanced buckets and increased sorting time. In our research, we explore how combinatorial algorithms can enhance Bucket Sort’s efficiency by optimizing bucket partitioning, dynamic allocation, and internal sorting strategies. Through rigorous mathematical proofs and analysis, we demonstrate that the application of combinatorial techniques yields substantial improvements in average-case performance, particularly in handling skewed data distributions. Practical case studies in large-scale data processing illustrate the adaptability and effectiveness of these optimizations, supporting their potential in real-world applications.