Normalized Weight Calculation for Dynamic Tree Structures
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Solution Overview
Problem
Processor-driven decision-making systems face inefficiencies when dealing with weighted trees, as they require recalculating the entire tree upon node modifications, leading to wasteful and redundant operations, and struggle with direct comparisons of node weights across different sibling groups.
Innovation Solution
The method involves determining normalized weights for nodes in weighted trees by calculating proportional weights and lesser unique sums, allowing for direct comparisons and reducing redundant calculations by caching these values, thereby improving performance and efficiency during tree modifications.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the entire weighted tree is recalculated upon node modifications, then the decision-making accuracy is maintained, but the computational time and processing efficiency deteriorate
Solution Approach 1:
The patent segments the weighted tree into independent nodes, each maintaining its own weight and normalized weight calculations. When a node is modified, only that specific node and its affected descendants need recalculation rather than the entire tree, thus maintaining accuracy while reducing computational time.
Solution Approach 2:
The patent pre-calculates and stores normalized weights for all nodes during tree construction. This preliminary action allows the system to quickly retrieve pre-computed values during decision-making processes, avoiding repeated full-tree calculations and significantly reducing processing time while maintaining decision accuracy.
2Ease of operation
If node weights are compared directly across different sibling groups, then the comparison simplicity is improved, but the measurement precision deteriorates due to different parent weights
Solution Approach 1:
The patent transforms the weight parameter by calculating normalized weights that incorporate the parent node's weight into the normalization factor. This parameter transformation allows direct comparison of normalized weights across different sibling groups while maintaining measurement precision, as each normalized weight is adjusted relative to its parent's weight context.
3Reliability
If redundant calculations are performed during tree modifications, then the calculation completeness is maintained, but the processing efficiency deteriorates
Solution Approach 1:
The patent extracts and caches the normalized weight values for each node separately from the main tree structure. This extraction allows the system to perform modifications by updating only the affected node's cached value and its descendants, maintaining calculation completeness while eliminating redundant calculations of unaffected portions of the tree.
Data Source
AI summary
Nodes of a weighted tree each have their own weight. A normalized weight of a node, relative to other nodes in the tree, is determined based on a proportional weight of the node and a lesser unique sum of the node, as well as those of the node's parents and grandparents, up to a root of the tree. The proportional weight and lesser unique sum of a given node depend only on the unique weights of the sibling group including the given node. Thus, if a weight is modified, the normalized weight can be updated without necessarily recalculating the entire tree.