Memory-Efficient Parallel Community Detection on Large Graphs Using Weighted Sketches: A Trade-off Between Speed and Memory Usage

핵심 개념

This paper introduces a memory-efficient approach to parallel community detection in large graphs, utilizing weighted Misra-Gries sketches to reduce the memory footprint of Louvain, Leiden, and Label Propagation Algorithms (LPA) at the cost of moderate runtime increase.

초록

• Bibliographic Information: Sahu, S. (2024). Memory-Efficient Community Detection on Large Graphs Using Weighted Sketches. arXiv preprint arXiv:2411.02268v1.
• Research Objective: This paper aims to address the memory constraints of community detection algorithms on large graphs by proposing memory-efficient alternatives to the Louvain, Leiden, and LPA algorithms.
• Methodology: The authors propose replacing the collision-free per-thread hashtables used in their previous implementations of Louvain, Leiden, and LPA with weighted Misra-Gries (MG) sketches. This approach focuses on identifying and storing information only for the most significant neighboring communities, thereby reducing memory usage. The performance of the modified algorithms is evaluated on a dataset of 13 large real-world graphs from the SuiteSparse Matrix Collection.
• Key Findings: The use of weighted MG sketches significantly reduces the memory footprint of the Louvain, Leiden, and LPA algorithms, with a minimal impact on the quality of the detected communities. However, this reduction in memory usage comes at the cost of increased runtime. The MG-based Louvain and LPA algorithms with 8 slots and the MG-based Leiden algorithm with 64 slots show the best trade-off between runtime and community quality.
• Main Conclusions: The proposed memory-efficient approach using weighted MG sketches offers a viable solution for community detection in large graphs, especially when memory resources are limited. While the modified algorithms are slower than their default counterparts, they maintain comparable community quality.
• Significance: This research contributes to the field of community detection by addressing the memory bottleneck of existing algorithms, making it possible to analyze larger graphs on shared-memory systems.
• Limitations and Future Research: The study primarily focuses on undirected, weighted graphs. Future research could explore the applicability of the proposed approach to directed and unweighted graphs. Additionally, investigating further optimizations to reduce the runtime overhead introduced by using MG sketches could be beneficial.

통계

The MG-based Louvain algorithm with 8 slots is, on average, 2.07× slower than the default Louvain algorithm on web graphs.
The MG-based Leiden algorithm with 64 slots runs 3.19× slower than the default Leiden algorithm.
The MG-based LPA algorithm with 8 slots is 2.11× slower than the default LPA algorithm.

인용구

핵심 통찰 요약

Memory-Efficient Community Detection on Large Graphs Using Weighted Sketches

by Subhajit Sah... 게시일 arxiv.org 11-05-2024

https://arxiv.org/pdf/2411.02268.pdf

더 깊은 질문

How does the performance of the proposed memory-efficient algorithms compare to other memory-reduction techniques used in community detection, such as graph coarsening or streaming algorithms?

The authors primarily focus on reducing the memory footprint of the Louvain, Leiden, and LPA algorithms while preserving the quality of detected communities, as measured by modularity. This differs from other memory reduction techniques like graph coarsening and streaming algorithms, which often involve trade-offs in community quality for reduced memory usage.
Here's a comparison:

Graph Coarsening: This technique reduces memory demands by creating a smaller graph that approximates the original. While it reduces memory usage and runtime, it can lead to a loss of information and potentially lower the quality of detected communities. The authors' approach, using weighted MG sketches, aims to minimize this quality loss by focusing on the most significant neighboring communities.

Streaming Algorithms: These algorithms process edges sequentially in a single pass, making them highly memory-efficient. However, the single-pass constraint can limit the quality of detected communities compared to multi-pass algorithms like Louvain and Leiden. The authors acknowledge this limitation and focus on improving the memory efficiency of these multi-pass algorithms without sacrificing community quality.
In essence, the authors' approach targets a specific niche: improving the memory efficiency of established multi-pass community detection algorithms while minimizing the compromise on community quality. This differs from techniques like graph coarsening and streaming algorithms, which prioritize memory reduction over community quality or operate under different constraints. A direct comparison of performance would require evaluating all methods on the same dataset and comparing not only runtime and memory usage but also the quality of the detected communities.

Could the authors achieve further runtime improvements by exploring alternative data structures or optimization techniques for the weighted MG sketch implementation?

Yes, the authors could potentially achieve further runtime improvements by exploring alternative data structures or optimization techniques for the weighted MG sketch implementation. Here are a few possibilities:

Alternative Data Structures: Instead of a simple array-based implementation of the MG sketch, using data structures like a binary heap or a hash table with open addressing could potentially speed up the insertion and search operations within the sketch. For instance, a min-heap could be used to efficiently track the minimum count in the sketch, allowing for faster decrement operations.

Parallelization of Sketch Operations: While the authors use OpenMP for parallelization, further runtime improvements might be possible by exploring fine-grained parallelization of the MG sketch operations themselves. For example, the insertion and decrement operations on the sketch could potentially be parallelized, especially for vertices with a large number of neighbors.

Adaptive Slot Allocation: The authors use a fixed number of slots (k) for the MG sketch. Dynamically adjusting k based on the characteristics of the graph or the progress of the algorithm could lead to better performance. For instance, k could be initially set high and then gradually decreased as the algorithm converges, potentially reducing unnecessary computations.

Exploiting Graph Structure: The authors' current implementation treats all vertices uniformly. However, real-world graphs often exhibit heterogeneous degree distributions and community structures. Adapting the MG sketch implementation to exploit such structural properties could lead to runtime improvements. For example, using a smaller k for vertices in dense regions of the graph might be sufficient, while vertices in sparse regions might benefit from a larger k.
By investigating these and other potential optimizations, the authors could potentially further enhance the runtime performance of their memory-efficient community detection algorithms.

How can the insights from this research be applied to develop more efficient algorithms for other graph-based problems that face similar memory constraints when dealing with large datasets?

The insights from this research, particularly the use of weighted MG sketches to approximate key information while maintaining accuracy, can be extended to other graph-based problems facing memory constraints. Here are a few examples:

Graph Clustering and Partitioning: Similar to community detection, graph clustering and partitioning algorithms often require storing and updating large amounts of information about vertex relationships. Weighted MG sketches could be used to approximate these relationships, reducing memory usage while potentially maintaining the quality of the resulting clusters or partitions.

Centrality Measures: Computing centrality measures like betweenness centrality or closeness centrality can be memory-intensive for large graphs. Weighted MG sketches could be employed to approximate the contributions of different paths or distances, enabling more memory-efficient computation of these measures.

Link Prediction: Link prediction algorithms often rely on analyzing the neighborhood structure of vertices to predict missing or future links. Weighted MG sketches could be used to efficiently represent and update these neighborhood structures, reducing memory requirements while potentially maintaining prediction accuracy.

Frequent Subgraph Mining: Identifying frequent subgraphs in large graphs is a memory-intensive task. Weighted MG sketches could be adapted to efficiently track the occurrences of different subgraphs, enabling more scalable frequent subgraph mining.

Graph Embedding: Graph embedding methods aim to learn low-dimensional vector representations of vertices while preserving their structural relationships. Weighted MG sketches could be incorporated into these methods to approximate these relationships during the embedding process, potentially reducing memory usage and speeding up computations.
The key takeaway is that the weighted MG sketch, as a method for approximating important information in a memory-efficient manner, can be a valuable tool for developing scalable algorithms for various graph-based problems. By adapting the principles and techniques presented in this research, researchers can potentially address memory constraints in other graph algorithms while striving to maintain the accuracy and effectiveness of their solutions.