Binary Edge Labeled Trees for Hierarchical Data Enumeration
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Solution Overview
Problem
Manipulating complex hierarchical data structures, such as relational databases, is computationally complex and cumbersome, necessitating more efficient techniques for operations like merging, splitting, and ordering.
Innovation Solution
The use of binary edge labeled trees (BELTs) and their enumeration methods, which convert complex hierarchical data into numerical data for easier manipulation, using techniques like zero-push and one-push operations, and table lookups to associate natural numerals with BELTs, enabling efficient operations like multiplication and factorization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If complex hierarchical data structures are manipulated directly, then the data relationships are preserved, but the computational complexity increases and operations become cumbersome
Solution Approach 1:
The patent introduces an intermediary representation system that maps hierarchical data structures to a simplified numerical format. BELTs serve as the intermediary that captures essential hierarchical relationships while enabling efficient numerical operations. The mapping process transforms complex tree structures into numerical sequences that can be manipulated through simple arithmetic operations, thus reducing computational complexity while preserving structural information.
Solution Approach 2:
The patent changes the parameter representation of hierarchical data from structural descriptors to numerical values. By encoding hierarchical relationships as numerical sequences and using operations like zero-push and one-push to modify these parameters, the system enables efficient manipulation of data hierarchies through parameter transformation rather than structural reconfiguration.
2Loss of information
If hierarchical data is represented in detailed structural form, then relationships between data elements are explicit, but manipulation operations become computationally expensive
Solution Approach 1:
The patent creates a simplified copy or representation of the hierarchical data structure in numerical form. BELTs serve as a copy that preserves the essential relationships and structure of the original hierarchical data while enabling efficient numerical manipulation. This copying approach allows operations to be performed on the numerical representation without directly manipulating the complex original structure, thus improving computational efficiency while maintaining relationship integrity.
3Measurement precision
If traditional methods are used to perform operations on hierarchical data, then accuracy is maintained, but the processes are cumbersome and time-consuming
Solution Approach 1:
The patent substitutes mechanical or structural manipulation methods with numerical computation methods. Instead of physically reconfiguring hierarchical data structures through complex algorithms, the system uses numerical operations on BELTs to achieve the same manipulations. This substitution replaces time-consuming structural operations with efficient arithmetic computations, reducing manipulation time while maintaining operational accuracy through the mathematically rigorous numerical framework.
Data Source
AI summary
Embodiments of methods, apparatuses, devices and/or systems for manipulating hierarchical sets of data are disclosed. In particular, methods, apparatus devices and or/or systems for enumerating rooted partial subtrees are disclosed.