Hexadecimal Routing Data Structure for Constant Time Operations
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing data structures, such as hash maps, binary trees, and linked lists, exhibit variable worst-case time complexities from O(n) to O(log(n)) or O(n/m), making them inefficient for managing data in highly responsive and real-time environments, leading to costly computational usage and high run times.
Innovation Solution
A data structure system that uses a hexadecimal digit-based routing mechanism to insert, search, and delete nodes within a data structure, achieving constant time complexity of O(32) for operations by limiting traversals through a system comprising processors and non-transitory computer-readable storage encoding instructions, allowing for efficient data management and traversal.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If traditional data structures (hash maps, binary trees, linked lists) are used, then data can be stored and accessed, but the time complexity varies from O(n) to O(log(n)) resulting in high run times and costly computational usage
Solution Approach 1:
The data structure is segmented into multiple levels (e.g., L0, L1, L2, ...) where each level contains a fixed number of nodes (e.g., 16 nodes per level). This segmentation allows the traversal to be limited to a constant number of levels regardless of the total data size, achieving O(32) time complexity by dividing the data space into manageable hierarchical segments.
Solution Approach 2:
The patent introduces a hierarchical dimensional structure with multiple levels instead of a single-dimensional linear structure. By organizing data across vertical levels and horizontal nodes within each level, the traversal complexity is bounded by the number of levels (constant depth), transforming the problem from linear/O(log n) traversal to constant-depth hierarchical traversal.
2Speed
If data structures with variable time complexity are used, then flexibility in data storage is maintained, but real-time responsiveness is compromised due to O(n) to O(log(n)) complexity
Solution Approach 1:
The patent changes the structural parameters of the data structure by fixing the number of nodes per level (e.g., 16 nodes) and limiting the number of levels (e.g., 32 levels maximum). This parameter fixation ensures that traversal operations are bounded by a constant number of steps, achieving real-time responsiveness with O(32) complexity while maintaining organized data storage.
3Productivity
If hierarchical levels are added to limit traversals, then traversal speed improves to constant time, but the data structure becomes more complex
Solution Approach 1:
The data structure is pre-organized into a hierarchical framework with a predetermined maximum number of levels and fixed nodes per level before data insertion. This preliminary structural setup ensures that future traversal operations can proceed efficiently with bounded steps, as the path length is predetermined by the hierarchical depth rather than the total data volume.
Data Source
AI summary
A data structure is specialized in efficiently representing a key-value pair in a highly optimized way. The data structure is a pointer in a traversal graph that takes advantage of constant time traversal for all operations. The data structure has specific instructions for inserting data nodes, router nodes, and how the expansion or collapse of the graph works. The data structure can be applied where the time to get the result back is most prominent. The data structure can be used to reduce the memory footprint to reach the data that is being searched and achieve a worst-case time complexity in constant time.