[Paper Review] Efficient Bitruss Decomposition for Large-scale Bipartite Graphs

Kai Wang, Xuemin Lin+3 more|arXiv (Cornell University)|Jan 16, 2020

Data Mining Algorithms and Applications25 references4 citations

TL;DR

This paper proposes efficient algorithms, BiT-BU and BiT-PC, for bitruss decomposition in large-scale bipartite graphs by introducing the BE-Index, a novel online index that compresses butterflies into k-blooms. The approach reduces time complexity and accelerates decomposition by up to two orders of magnitude on real-world datasets, significantly outperforming prior methods.

ABSTRACT

Cohesive subgraph mining in bipartite graphs becomes a popular research topic recently. An important structure k-bitruss is the maximal cohesive subgraph where each edge is contained in at least k butterflies (i.e., (2, 2)-bicliques). In this paper, we study the bitruss decomposition problem which aims to find all the k-bitrusses for k >= 0. The existing bottom-up techniques need to iteratively peel the edges with the lowest butterfly support. In this peeling process, these techniques are time-consuming to enumerate all the supporting butterflies for each edge. To relax this issue, we first propose a novel online index -- the BE-Index which compresses butterflies into k-blooms (i.e., (2, k)-bicliques). Based on the BE-Index, the new bitruss decomposition algorithm BiT-BU is proposed, along with two batch-based optimizations, to accomplish the butterfly enumeration of the peeling process in an efficient way. Furthermore, the BiT-PC algorithm is devised which is more efficient against handling the edges with high butterfly supports. We theoretically show that our new algorithms significantly reduce the time complexities of the existing algorithms. Also, we conduct extensive experiments on real datasets and the result demonstrates that our new techniques can speed up the state-of-the-art techniques by up to two orders of magnitude.

Motivation & Objective

• Address the performance bottleneck in existing bottom-up bitruss decomposition algorithms caused by expensive butterfly enumeration during edge peeling.
• Enable scalable analysis of large-scale bipartite graphs—common in social networks, recommendation systems, and scholarly networks—by reducing computational overhead.
• Develop a novel online indexing structure, BE-Index, to compress and efficiently manage butterfly supports for dynamic edge processing.
• Design optimized algorithms, BiT-BU and BiT-PC, that minimize redundant butterfly support updates and improve performance on high-degree (hub) edges.
• Achieve significant speedups over existing state-of-the-art techniques while maintaining correctness and scalability on real-world graphs.

Proposed method

• Introduce the BE-Index, an online index that compresses all butterflies in a bipartite graph into k-blooms (i.e., (2,k)-bicliques), enabling efficient butterfly support tracking.
• Design the BiT-BU algorithm, a bottom-up decomposition method that leverages the BE-Index to avoid repeated butterfly enumeration during edge peeling.
• Integrate two batch-based optimizations: batch edge processing and batch bloom processing, to reduce the number of updates and improve cache efficiency.
• Propose BiT-PC, a progressive compression-based algorithm that processes high-support edges first, compressing the graph iteratively to reduce subsequent butterfly support updates.
• Use a parameter τ in BiT-PC to control the rate of graph compression, balancing iteration count and update overhead for optimal performance.
• Theoretical analysis shows that BiT-BU and BiT-PC achieve lower time complexity than prior methods by reducing redundant butterfly counting and update operations.

Experimental results

Research questions

• RQ1 How can we reduce the time complexity of bitruss decomposition in large-scale bipartite graphs by minimizing repeated butterfly enumeration during edge peeling?
• RQ2 Can we design an online indexing structure that efficiently captures and compresses butterfly supports to accelerate decomposition?
• RQ3 What optimizations can be applied to the bottom-up decomposition pipeline to reduce update overhead and improve performance on large graphs?
• RQ4 How does progressive graph compression in BiT-PC improve performance on edges with high butterfly support compared to standard peeling?
• RQ5 What is the optimal configuration of the compression parameter τ in BiT-PC for balancing iteration count and update cost across diverse real-world datasets?

Key findings

• The proposed BiT-BU and BiT-PC algorithms achieve up to two orders of magnitude speedup over the state-of-the-art algorithm on real-world datasets such as Wiki-it and D-style.
• On the Wiki-it dataset with over 600 million butterflies, the BE-Index data structure consumes less than 4GB of main memory, demonstrating strong space efficiency.
• The batch-based optimizations in BiT-BU++ reduce both computation cost and the number of support updates, with batch bloom processing providing the most significant performance gain.
• BiT-PC outperforms BiT-BU and BiT-BU++ on large datasets like D-style and Wiki-it by processing hub edges within more cohesive subgraphs, reducing subsequent updates by over 90%.
• The parameter τ in BiT-PC has a minimal impact on performance when set between 0.05 and 0.2, indicating robustness and ease of tuning across diverse graph structures.