Graph Generation Using Recursive Vectors and Lookup Tables
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Solution Overview
Problem
Current synthetic graph generators are inefficient in terms of space and time complexities, making it challenging to generate large-scale realistic graphs, especially trillion-scale graphs, using a small amount of computing resources, and lack scalability for generating semantically rich graph models.
Innovation Solution
A graph generating method that uses a recursive vector model to efficiently generate massive graphs by reusing pre-computed vectors, reducing quadrant selections, and minimizing random value generations, allowing for scalable and fast graph generation using a small amount of memory.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If RMAT or Kronecker models are used to generate synthetic graphs, then the graphs can achieve power-law degree distribution and realistic properties, but the time complexity and space complexity increase significantly, making it impossible to generate trillion-scale graphs on commodity machines
Solution Approach 1:
The patent pre-calculates and stores the cumulative probability values in a lookup table before graph generation. This preliminary action eliminates the need for repeated probability calculations during edge generation, reducing time complexity from O(log |V|) per edge to O(1) per edge, enabling trillion-scale graph generation on commodity machines while maintaining realistic power-law degree distribution
Solution Approach 2:
The patent uses a compact lookup table that stores pre-computed probability values as a simplified representation of the full probability distribution. This copying approach replaces complex recursive probability calculations with simple table lookups, significantly improving generation speed while preserving the realistic graph properties through accurate probability sampling
2Reliability
If RMAT or Kronecker models are used to generate synthetic graphs, then the graphs can achieve power-law degree distribution and realistic properties, but the memory requirement increases, requiring supercomputers instead of commodity machines
Solution Approach 1:
The patent extracts only the essential probability information needed for edge generation into a compact lookup table. By taking out only the necessary cumulative probability values and storing them in a space-efficient format, the patent reduces memory requirements from terabytes to megabytes, enabling graph generation on commodity machines while maintaining realistic power-law degree distribution
Solution Approach 2:
The patent changes the representation parameters of the probability distribution from storing full recursive probability matrices to storing compact cumulative probability values in a lookup table. This parameter transformation reduces space complexity while preserving the ability to generate edges with correct probability distributions, enabling trillion-scale graph generation with limited memory
3Reliability
If recursive quadrant selection is performed for each edge generation in RMAT, then the graphs can achieve realistic properties, but the computational overhead increases due to repeated random value generations and quadrant selections
Solution Approach 1:
The patent pre-computes and stores cumulative probability values in a lookup table before graph generation. This preliminary action eliminates the need for repeated random value generations and quadrant selections during edge generation, reducing computational overhead from O(log |V|) operations per edge to O(1) operations per edge, while maintaining realistic graph properties through accurate probability sampling
Solution Approach 2:
The patent skips the repeated recursive quadrant selection process by using pre-computed lookup tables. Instead of performing multiple random value generations and quadrant selections for each edge, the patent directly retrieves the destination vertex from the lookup table, rushing through the generation process while maintaining realistic graph properties
Data Source
AI summary
Disclosed is a graph generating method and apparatus, the graph generating apparatus that may recognize one source vertex among a plurality of vertices, obtain the target number of at least one edge to generate from the source vertex, among the total target number of edges to generate between the vertices, obtain a recursive vector to be used repeatedly to generate the at least one edge, in a scope in which an existence of an edge for the source vertex needs to be verified, and generate the at least one edge between the source vertex and at least one destination vertex based on the target number and the recursive vector.