Tree Data Structure Linear Chain Segmentation for Query Traversal
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Solution Overview
Problem
Existing traversal algorithms for tree data structures are inefficient when dealing with large numbers of nodes, as they often require traversing significant portions of the tree, consuming substantial time and computational resources, especially when the path between queried nodes is not directly connected.
Innovation Solution
Divide the tree data structure into multiple linear chains of nodes, where each chain has at most a single parent and child node, allowing for more efficient traversal by selecting and backtracking within these chains, reducing time complexity to O(log(N)) compared to O(E Log(N)) or O(|N|) of traditional algorithms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional traversal algorithms are used on the entire tree data structure, then complete path information can be obtained, but the time complexity is O(E Log(N)) or O(|N|) which is inefficient for large trees
Solution Approach 1:
The patent divides the tree data structure into multiple linear chains, where each chain contains a subset of nodes arranged in a linear sequence. This segmentation allows the traversal algorithm to operate on smaller, more manageable chain structures rather than the entire tree, reducing the time complexity from O(E Log(N)) or O(|N|) to O(log(N)) while still maintaining the ability to compute accurate path sums by combining results from relevant chains.
2Measurement precision
If the tree is traversed to find the shortest path between two nodes, then accurate path sum can be calculated, but substantial computational resources are consumed
Solution Approach 1:
By segmenting the tree into linear chains, the patent reduces the computational scope from the entire tree to specific chain segments that are relevant to the query. This allows the algorithm to calculate path sums by traversing only the necessary chains and combining their results, significantly reducing computational resource consumption while maintaining calculation accuracy.
Solution Approach 2:
The patent applies partial action by traversing only the specific linear chains that contain the path between the two queried nodes, rather than performing a complete tree traversal. This partial traversal approach computes the required path sum by processing only the relevant subset of nodes and edges, thereby reducing energy and computational resource usage.
3Adaptability or versatility
If traditional tree traversal is performed, then all nodes can be visited, but the number of computations increases significantly with large numbers of nodes
Solution Approach 1:
The patent segments the tree into linear chains, enabling the algorithm to adapt to different tree structures by organizing nodes into appropriate chain configurations. This segmentation maintains versatility in handling various tree topologies while improving productivity by reducing the number of computations required, as the algorithm only needs to traverse relevant chains rather than the entire tree structure.
Data Source
AI summary
Described are techniques for efficiently traversing a tree data structure to determine responses to queries by first dividing the tree data structure into linear chains of nodes. Linear chains may be formed by beginning at an initial node, including the child node of the initial node that has the largest number of descendant nodes, and proceeding to include child nodes associated with the largest number of descendant nodes until a node lacking child nodes is reached. Additional chains may then be formed by beginning at an initial node not included in previous linear chains and repeating the process. Responsive to a received query, traversal of each linear chain encountered along a query path may be performed more efficiently than other traversal algorithms that traverse a tree data structure until an end node is reached.