Graph-Integrated Tree Traversal for O(1) Lateral Node Access
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Solution Overview
Problem
Existing tree-based representations restrict direct lateral traversal between nodes in the same layer, leading to slow search times with a time complexity of O(log N) due to the need for upward and downward traversals.
Innovation Solution
Integrate a graph structure with each layer of the tree-based representation, providing pointers, indices, or hash maps to enable direct lateral traversal without vertical movements, resulting in O(1) time complexity for searches.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If traditional tree-based representation is used, then data is hierarchically organized with ordered access, but lateral traversal between nodes in the same layer is slow requiring upward and downward movements
Solution Approach 1:
The patent merges a graph structure with the tree-based representation by integrating graph nodes at each layer with the tree nodes. This combination allows lateral traversal through graph edges while preserving the hierarchical organization of the tree, thereby improving traversal speed without losing the benefits of tree structure.
Solution Approach 2:
The patent introduces graph nodes as intermediary elements between tree nodes in the same layer. These graph nodes act as mediators that enable direct lateral connections between nodes that would otherwise require upward and downward traversal through the tree structure, significantly improving lateral access speed.
2Loss of time
If direct lateral traversal is implemented, then search time complexity improves to O(1), but additional graph structure integration is required
Solution Approach 1:
The patent adds a lateral dimension to the traditional vertical tree structure by integrating graph nodes and edges. This dimensional transformation enables O(1) lateral access by creating horizontal pathways alongside the existing vertical hierarchical paths, effectively adding another dimension to the data access model.
3Stability of the object's composition
If upward and downward traversals are performed for lateral access, then tree structure is maintained, but access efficiency decreases
Solution Approach 1:
The patent segments the data access pathways into two distinct types: vertical tree-based paths for hierarchical navigation and horizontal graph-based paths for lateral traversal. This segmentation allows each structure to optimize for its intended access pattern, maintaining tree integrity while improving overall access efficiency.
Data Source
AI summary
Disclosed is an encoding system and associated methods for generating a graph-integrated tree-based representation of data that provides for direct lateral traversals of nodes in a each layer of the tree-based representation. The encoding system organizes data from a dataset to a tree-based representation with multiple layers and multiple nodes in each layer. The encoding system detects the nodes in each layer, and defines a graph structure that links the nodes in each layer for direct lateral access. The encoding system searches the tree-based representation in response to a query for a particular subset of the data by performing a single downward traversal to a particular layer with individual nodes that satisfy part of the query, and by laterally traversing the nodes in the particular layer using the graph structure to directly access a second node in the particular layer from a first node in the particular layer.