Efficient Workload-balanced Push-Relabel Algorithm for Massive Graphs on GPUs

Core Concepts

The authors propose a workload-balanced push-relabel algorithm (WBPR) with enhanced compressed sparse representations (CSR) to efficiently process massive graphs on GPUs. WBPR reduces memory consumption and alleviates workload imbalance to achieve significant speedups over the state-of-the-art.

Abstract

The paper addresses the challenges of processing massive graphs using the push-relabel algorithm on GPUs. The authors identify two key issues: 1) the significant memory consumption of representing the residual graph, and 2) the inherent workload imbalance in the traditional parallel push-relabel algorithm.
To address the memory consumption challenge, the authors propose two enhanced CSR data structures - Reversed CSR (RCSR) and Bidirectional CSR (BCSR). RCSR reduces the memory complexity from O(V^2) to O(V+E) by storing backward edges separately. BCSR further improves memory access efficiency by aggregating incoming and outgoing neighbors.
To tackle the workload imbalance, the authors introduce a novel vertex-centric approach with two-level parallelism. First, all threads are used to scan the vertices and add active ones to an Active Vertex Queue (AVQ). Then, a tile of threads is assigned to process each active vertex, allowing them to parallelize the search for the minimum-height neighbor vertex.
The authors evaluate their WBPR algorithm on both maximum flow and bipartite matching tasks using real-world and synthetic graphs. Compared to the state-of-the-art, WBPR achieves up to 7.31x and 2.29x speedups on maximum flow and bipartite matching, respectively, by effectively reducing memory consumption and balancing the workload on the GPU.

Stats

The maximum flow value of the Washington-RLG graph is 262,146.
The maximum flow value of the Genrmf graph is 2,097,152.

Quotes

"The push-relabel algorithm is an efficient algorithm that solves the maximum flow/ minimum cut problems of its affinity to parallelization."
"To accommodate massive graphs in a GPU, we proposed RCSR and BCSR, which significantly reduce space complexity from O(V^2) to O(V + E) with trivial overhead on the process of the push-relabel algorithm."
"The novel vertex-centric approach can alleviate the workload imbalance among threads and improve the utilization of the GPU."

Key Insights Distilled From

Engineering A Workload-balanced Push-Relabel Algorithm for Massive Graphs on GPUs

by Chou-Ying Hs... at arxiv.org 04-02-2024

https://arxiv.org/pdf/2404.00270.pdf

Deeper Inquiries

How can the proposed WBPR algorithm be extended to handle dynamic graphs, where the graph structure changes over time

To extend the WBPR algorithm to handle dynamic graphs, where the graph structure changes over time, several modifications and considerations need to be made. One approach could involve implementing dynamic data structures that can efficiently update the graph representation as edges and vertices are added or removed. This would require incorporating mechanisms for dynamic memory allocation and deallocation to accommodate the changing graph size. Additionally, the algorithm would need to include strategies for updating the flow values and heights of vertices in real-time as the graph evolves. Techniques like incremental updates and efficient data structures such as dynamic arrays or linked lists could be employed to manage the changing graph structure effectively. Moreover, the algorithm may need to incorporate heuristics or algorithms for detecting and handling structural changes in the graph to ensure accurate flow computations despite the dynamic nature of the graph.

What are the potential limitations or trade-offs of the RCSR and BCSR representations, and how could they be further optimized for specific graph characteristics

The RCSR and BCSR representations, while effective in reducing memory consumption and optimizing memory access patterns for different graph characteristics, have potential limitations and trade-offs. One limitation is the increased complexity in managing and updating the compressed sparse representations as the graph evolves, especially in dynamic graph scenarios. The trade-offs include the overhead of maintaining additional data structures for backward edges in RCSR and the potential uncoalesced memory access in BCSR due to the discontinuous storage of neighbors. To further optimize these representations, specific strategies can be employed. For RCSR, optimizing the data structures for efficient updates and minimizing the overhead of managing backward edges could enhance its performance. For BCSR, improving memory access patterns through better sorting or indexing mechanisms could reduce the impact of uncoalesced memory access. Additionally, exploring hybrid representations that combine the strengths of RCSR and BCSR based on the graph characteristics could provide a more versatile and efficient solution.

Could the insights from this work on workload balancing be applied to other parallel graph algorithms beyond the push-relabel algorithm

The insights gained from this work on workload balancing in the context of the push-relabel algorithm can be applied to other parallel graph algorithms to improve their performance and scalability. By adopting a vertex-centric approach and implementing workload-balanced strategies, parallel graph algorithms can achieve better utilization of resources and enhanced efficiency. Techniques such as two-level parallelism, active vertex queues, and optimized memory access patterns can be generalized to various parallel graph algorithms to address workload imbalance issues and improve overall execution times. Additionally, the concept of workload distribution analysis and synchronization optimization can be extended to different parallel algorithms to enhance their parallelism and scalability on GPU architectures. By incorporating these insights, other parallel graph algorithms can benefit from improved performance and better resource utilization in large-scale graph processing tasks.