Dynamic Graph Modeling with Binary Decision Diagrams
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Solution Overview
Problem
Dynamic graphs, such as social network graphs, grow large and require significant memory and computational resources for storage and information extraction, making it expensive to manage and query their data efficiently.
Innovation Solution
Modeling dynamic graphs using Binary Decision Diagrams (BDDs) allows for compact storage and efficient information extraction by representing edges with characteristic functions and using threshold functions to manage edge existence over time, reducing memory footprint and query operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If dynamic graphs are stored using traditional data structures, then the graph can represent arbitrary node and edge relationships, but the memory usage and computational resources required for storage and information extraction become prohibitively large
Solution Approach 1:
The patent transforms the graph representation by changing parameters: nodes are encoded using binary representations of their identifiers, and edges are represented through characteristic functions that evaluate to boolean values. This parameter transformation enables compact storage while maintaining the ability to represent arbitrary graph structures.
Solution Approach 2:
The patent extracts the essential properties of graph relationships into characteristic functions g(t; a; b) that determine edge existence between nodes a and b at time t. By separating the edge existence logic into evaluable functions rather than storing complete adjacency information, the representation achieves compression while preserving query capabilities.
2Productivity
If traditional graph storage methods are used, then all graph information can be stored explicitly, but information extraction requires significant computational resources and time
Solution Approach 1:
The patent replaces traditional mechanical graph traversal and search operations with binary decision diagram evaluations. The characteristic functions and BDD structures enable information extraction through efficient binary operations rather than linear scanning or complex graph algorithms, dramatically improving extraction speed while reducing computational resource requirements.
3Adaptability or versatility
If the graph size increases to accommodate more nodes and edges, then the graph can model larger dynamic systems, but the memory footprint and query complexity increase exponentially
Solution Approach 1:
The patent merges multiple graph snapshots across different time points into a single unified BDD structure. By combining temporal information with graph structure in the characteristic functions, the system can model arbitrarily large dynamic graphs without proportionally increasing memory footprint, as the BDD structure shares common substructures across different time points and graph configurations.
Data Source
AI summary
In one embodiment, a dynamic graph having a plurality of nodes is modeled with a Binary Decision Diagram (BDD). Each pair of nodes in the dynamic graph is modeled using a characteristic function, g({right arrow over (t)};{right arrow over (a)};{right arrow over (b)}), where: {right arrow over (t)} denotes a time; {right arrow over (a)} denotes a first node identifier; {right arrow over (b)} denotes a second node identifier; and g evaluates to 1 (or TRUE) if and only if an edge exists and connects nodes {right arrow over (a)} and {right arrow over (b)} at time {right arrow over (t)}. The BDD is a combination of all the characteristic functions corresponding to all unique pairs of nodes in the dynamic graph.