Directed Graph Compression via Node Reordering
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Solution Overview
Problem
The growing scale of directed graphs poses challenges for efficient graph computation due to high graph size and storage costs, with current compression methods offering low compression ratios and high decompression overhead.
Innovation Solution
A method involving node reordering and adjacency matrix encoding, where non-zero elements are clustered and represented by integers, reducing graph size by minimizing non-empty blocks and encoding them efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If current compression methods are used for directed graphs, then storage costs are reduced, but compression ratios are low and decompression overhead is high
Solution Approach 1:
The adjacency matrix is divided into multiple blocks, where each block represents a sub-matrix of the original graph. This segmentation allows independent processing and compression of each block, reducing the overall decompression overhead while achieving better compression ratios through targeted optimization of each block's structure.
Solution Approach 2:
The graph nodes are reordered using a specific algorithm before compression to cluster non-zero elements together. This preliminary reordering action ensures that the adjacency matrix has a more compact structure with larger contiguous blocks of non-zero elements, which significantly improves both compression ratio and reduces decompression overhead by minimizing the number of blocks that need to be processed.
2Quantity of substance
If graph scale increases, then more nodes and edges can be represented, but storage costs and computation efficiency deteriorate
Solution Approach 1:
The invention changes the structural parameters of the graph representation by reordering nodes to optimize the adjacency matrix structure. This reordering transforms the distribution of non-zero elements, creating a more compact representation that reduces storage requirements while maintaining the ability to represent large-scale graphs with millions of nodes and edges.
Data Source
AI summary
In one embodiment of the present disclosure, an original graph including nodes is obtained. The nodes of the original graph are reordered to generate a reordered graph. Non-zero elements in an adjacency matrix for the reordered graph are clustered as compared with an adjacency matrix for the original graph. The adjacency matrix for the reordered graph is encoded with integers. The integers correspond to non-empty blocks in the adjacency matrix for the reordered graph.