K-Segmented Search: A Novel Multi-Pointer Algorithm for Large-Scale Ordered Data

This research paper introduces the K-Segmented Search Algorithm (KSSA) — a new generalization of classical binary and ternary search algorithms designed for large-scale ordered datasets. Unlike binary search, which splits data into two parts, or ternary search, which divides it into three, KSSA divides the dataset into K logical segments at each step. This allows for potential parallel or distributed searching, improving speed and scalability for massive data environments (like terabyte-scale systems). The paper presents: A detailed pseudocode and complexity analysis (best, worst, and average cases). A mathematical proof showing that the optimal segment count (K) is 3, aligning with the efficiency of ternary search. A quantitative and experimental evaluation using Python implementations and numerical validation, confirming theoretical predictions. Practical implications for cache optimization, parallelism, and large database systems. Finally, the study concludes that while increasing K theoretically reduces search depth, it introduces extra comparison overhead — meaning ternary segmentation (K = 3) offers the best real-world balance between speed and complexity. The paper also suggests future work in parallelization, adaptive algorithms, and cache-aware optimization to extend KSSA’s efficiency in distributed computing environments.