Clique-Based Graph Compression for Faster Parallel Computation
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Solution Overview
Problem
Existing graph compression methods are inefficient in reducing computational time and storage requirements, as they often require significant computational effort to avoid using additional memory, and clique-finding algorithms are difficult to approximate and time-consuming.
Innovation Solution
A method and system that identify and remove large cliques from graphs to generate a compressed representation, using clique pseudo-vertices and ordering vertices based on k-core degeneracy values to improve storage efficiency and computational speed, allowing for faster graph computations and reduced memory usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If traditional graph compression methods are used, then storage requirements are reduced, but computational time increases significantly
Solution Approach 1:
The patent segments the graph into multiple cliques (fully connected subgraphs) and represents each clique separately. This segmentation allows the compressed representation to store only clique memberships rather than all individual edges, reducing storage requirements while enabling efficient computational operations by operating on clique-level abstractions.
Solution Approach 2:
The patent introduces clique pseudo-vertices as intermediaries between original graph vertices and the compressed representation. These pseudo-vertices serve as mediators that encode clique membership information, allowing efficient computation of graph properties without explicitly storing or processing all original edges, thus reducing both storage and computational time.
2Quantity of substance
If clique-finding algorithms are used to identify maximum cliques, then graph compression is achieved, but the algorithms are difficult to approximate and time-consuming
Solution Approach 1:
The patent performs preliminary actions by ordering vertices based on their degrees before applying clique-finding algorithms. This preprocessing step arranges vertices in a sequence that facilitates more efficient clique identification, reducing the computational complexity of the subsequent clique-finding process while maintaining effective compression ratios.
Solution Approach 2:
The patent changes the parameter of vertex ordering from arbitrary or simple indexing to degree-based ordering. This parameter change transforms the clique-finding process into a more efficient operation by ensuring that vertices with higher connectivity are processed first, which accelerates the identification of maximum cliques and reduces algorithmic complexity.
3Quantity of substance
If maximum cliques are removed from the graph iteratively, then compressed representation is generated, but vertices may need to be processed multiple times
Solution Approach 1:
The patent performs preliminary vertex ordering based on degrees before the iterative clique removal process. This preliminary action ensures that vertices are arranged in an optimal sequence, allowing the algorithm to efficiently identify and remove cliques in a single pass or minimal passes, thereby reducing the need to reprocess vertices multiple times while achieving effective compression.
Data Source
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AI summary
Embodiments of the present invention provide a system for fast parallel graph compression based on identifying a set of large cliques, which is used to encode the graph. The system provides both permanently-stored and in-memory graph encoding and reduces the space needed to represent and store a graph, the I/O traffic to use the graph, and the computation needed to perform algorithms involving the graph. The system thereby improves computing technology and graph computation. During operation, the system obtains data indicating vertices and edges of a graph. The system executes a clique-finding method to identify a maximum clique in the graph. The system then removes the clique from the graph, adds the clique to a set of found cliques, and generates a compressed representation of the graph based on the set of found cliques.