Approximate Vertex-Wise Maximal Clique Enumeration for Dynamic Graphs
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Solution Overview
Problem
Existing solutions for maximal clique enumeration in graphs are inefficient, particularly for dynamic graphs and real-time applications, as they often rely on exact determinations or tangential approaches that do not account for locally maximal groups for each entity of interest, and require user-defined size filters that may miss smaller but relevant cliques.
Innovation Solution
The proposed method, Approximate Vertex-Wise Maximal Clique Enumeration (AVMCE), computes an approximate one-to-many mapping of vertices to maximal cliques, focusing on locally maximal groups without user-defined size restrictions, and updates a data structure (CLIQUES) to reflect changes in dynamic graphs, allowing for real-time performance and efficient enumeration of all maximal cliques.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If exact maximal clique enumeration methods are used, then completeness of clique detection is improved, but computational time and complexity increase significantly
Solution Approach 1:
The patent applies partial action by computing approximate maximal cliques for each vertex rather than enumerating all maximal cliques exactly. The algorithm computes vertex-wise maximal cliques up to a user-specified size threshold, providing a practical approximation that balances completeness with computational feasibility for large graphs.
Solution Approach 2:
The patent changes the parameter of clique size by introducing a user-specified threshold parameter. This allows the algorithm to adaptively compute cliques of different sizes based on application requirements, enabling a trade-off between detection completeness and computational efficiency through parameter adjustment.
2Device complexity
If user-defined size filters are applied to reduce graph size, then computational complexity is reduced, but relevant smaller cliques may be missed
Solution Approach 1:
The patent inverts the traditional filtering approach by not filtering out small cliques but instead computing vertex-wise maximal cliques for all vertices regardless of size. The user-specified size parameter serves as a threshold for when to stop expanding cliques for each vertex, ensuring that relevant smaller cliques are not missed while still providing computational benefits.
3Measurement precision
If traditional clique enumeration methods are used on dynamic graphs, then accuracy of clique detection is maintained, but real-time performance is compromised
Solution Approach 1:
The patent applies dynamics by designing an algorithm specifically optimized for dynamic graphs that can efficiently handle graph updates. The vertex-wise maximal clique computation approach allows the algorithm to adapt to changing graph structures in real-time, maintaining accuracy while achieving the performance required for dynamic graph applications.
Data Source
AI summary
Discussed herein are devices, systems, and methods for determining an approximation of a set of largest maximal cliques containing each node, entities represented by nodes and pairwise relation represented by edges. The method can include receiving dynamic graph data indicating the nodes and the edges of a dynamic graph, estimating, for one or more nodes of the nodes, cliques of size less than (or equal to) a user specified or default clique size parameter, storing the estimated cliques in a clique variable, identifying, for cliques of size greater than (or equal to) the clique size parameter, at most a single clique of a corresponding size, storing the identified single clique in the clique variable, and returning, for each node, the largest maximal cliques in the clique variable.