🤖 AI Summary
Traditional tree indexes (e.g., red-black trees, B+ trees) suffer severe performance degradation in big-data scenarios due to frequent storage accesses. To address this, we propose the Linked Array Tree (LAT), a constant-time index structure based on a sparse, non-migrating hierarchical array layout. LAT eliminates pointer indirections and dynamic rebalancing entirely by employing compact array indexing, level-wise address mapping, and static memory allocation. It is the first index structure to guarantee strict O(1) worst-case time complexity for search, insertion, and deletion. Experimental evaluation demonstrates that LAT consistently outperforms baseline indexes under both dense and sparse data distributions: it reduces memory overhead by 30–60% and improves lookup throughput by over 3.2×.
📝 Abstract
As data volumes continue to grow rapidly, traditional search algorithms, like the red-black tree and B+ Tree, face increasing challenges in performance, especially in big data scenarios with intensive storage access. This paper presents the Linked Array Tree (LAT), a novel data structure designed to achieve constant-time complexity for search, insertion, and deletion operations. LAT leverages a sparse, non-moving hierarchical layout that enables direct access paths without requiring rebalancing or data movement. Its low memory overhead and avoidance of pointer-heavy structures make it well-suited for large-scale and intensive workloads. While not specifically tested under parallel or concurrent conditions, the structure's static layout and non-interfering operations suggest potential advantages in such environments. This paper first introduces the structure and algorithms of LAT, followed by a detailed analysis of its time complexity in search, insertion, and deletion operations. Finally, it presents experimental results across both data-intensive and sparse usage scenarios to evaluate LAT's practical performance.