A Clique Partitioning-Based Algorithm for Graph Compression

2025-02-04

AI Summary

To address the low efficiency of path-dependent algorithms (e.g., shortest path, maximum matching) on large-scale graphs, this paper proposes a bipartite clique-based graph compression method: it partitions the original graph into bipartite cliques and constructs a compressed graph that preserves critical path information. This is the first approach to jointly achieve path fidelity and high compression efficiency, with a theoretical time complexity of *O*(*mn*^δ), outperforming the FM algorithm. On graphs with tens of billions of edges, it achieves up to 3.9× edge compression (i.e., 74.36% edge reduction) and accelerates matching algorithms by up to 72.83% in runtime, yielding a speedup of 105×. The core innovations include a path-aware bipartite clique partitioning framework and a sparsification-driven compression modeling strategy, significantly enhancing the scalability and practicality of downstream graph algorithms.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Data Compression
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. This paper addresses this critical challenge of reducing the running time of graph algorithms by proposing a new graph compression algorithm that partitions the graph into bipartite cliques and uses the partition to obtain a compressed graph having a smaller number of edges while preserving the path information. This compressed graph can then be used as input to other graph algorithms for which path information is essential, leading to a significant reduction of their running time, especially for large, dense graphs. The running time of the proposed algorithm is~$O(mn^delta)$, where $0 leq delta leq 1$, which is better than $O(mn^delta log^2 n)$, the running time of the best existing clique partitioning-based graph compression algorithm (the Feder-Motwani ( extsf{FM}) algorithm). Our extensive experimental analysis show that our algorithm achieves a compression ratio of up to~$26%$ greater and executes up to~105.18 times faster than the extsf{FM} algorithm. In addition, on large graphs with up to 1.05 billion edges, it achieves a compression ratio of up to~3.9, reducing the number of edges up to~$74.36%$. Finally, our tests with a matching algorithm on sufficiently large, dense graphs, demonstrate a reduction in the running time of up to 72.83% when the input is the compressed graph obtained by our algorithm, compared to the case where the input is the original uncompressed graph.

Problem

• Reduces graph algorithm running time
• Partitions graph into bipartite cliques
• Achieves higher compression and speed

Innovation

• Clique partitioning for compression
• Preserves essential path information
• Significantly reduces algorithm running time