Sketch-Based Influence Estimation in Large Graphs
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Solution Overview
Problem
Existing methods for influence maximization in large graphs are computationally expensive and do not scale well, making it difficult to efficiently determine the influence of nodes and identify the most influential seed sets.
Innovation Solution
The use of combined reachability sketches or all-distances sketches generated for each node across multiple instances of a graph, allowing for the estimation of influence using a greedy algorithm, which reduces processing resources and improves scalability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the greedy algorithm is used for influence maximization, then the accuracy of influence estimation is improved, but the computational cost and time consumption increase significantly
Solution Approach 1:
The patent pre-generates multiple graph instances and computes reachability sketches for all nodes before the actual influence query is made. This preliminary computation stores intermediate results that can be quickly combined to answer influence queries without performing expensive edge traversals at query time, thus resolving the contradiction between accuracy and computational time.
Solution Approach 2:
The patent creates multiple copies of the graph with randomly instantiated edges according to the probabilistic model. Instead of traversing the original large graph repeatedly, it operates on these smaller copied instances and aggregates results, reducing the computational burden while maintaining estimation accuracy through the law of large numbers.
2Reliability
If the greedy algorithm is used for influence maximization, then the quality of seed set selection is improved, but the scalability to large graphs deteriorates
Solution Approach 1:
The patent segments the influence computation task into two parts: (1) pre-computation of reachability sketches for all nodes in multiple graph instances, and (2) combination of these sketches to estimate influence of any seed set. This segmentation allows the system to handle large graphs by distributing the computational work and enabling parallel processing, thus improving scalability while maintaining selection quality.
Solution Approach 2:
By pre-computing reachability information for all nodes before the influence maximization query, the patent eliminates the need for expensive edge traversals during the greedy selection process. This preliminary action enables the algorithm to scale to large graphs with millions of edges while maintaining the ability to make accurate greedy selections.
3Measurement precision
If multiple graph instances are generated and edge traversals are performed, then the accuracy of influence estimation is improved, but the computational resources required increase
Solution Approach 1:
The patent extracts only the essential reachability information from multiple graph instances and stores it in compact sketch data structures. Instead of performing full edge traversals and storing complete graph states, it extracts and stores only the necessary reachability counts, significantly reducing memory usage and computational resources while maintaining estimation accuracy.
Solution Approach 2:
The patent uses simplified copied representations (sketches) of graph instances rather than storing or processing the complete graph structures. These sketches contain only the essential reachability information needed for influence estimation, reducing the computational resources required to generate and process multiple graph instances while preserving accuracy.
Data Source
AI summary
A graph that includes multiple nodes and edges is received. Multiple instances of the graph are generated by randomly instantiating the edges according to either a binary independent cascade model or a randomized edge length independent cascade model. Where the binary independent cascade model is used, combined reachability sketches are generated for each node across all instances of the graph. Where the randomized edge length independent cascade model is used, combined all-distances sketches are generated for each node across all instances of the graph. Depending on which model is used, the combined reachability or all-distances sketches are used to estimate the influence of nodes in the graph or to estimate a subset of nodes from a graph of a specified size with a maximum influence using a greedy algorithm.