Minimum-cost flow problems widely exist in graph theory, computer science, information science, and transportation science. The network simplex algorithm is a fast and frequently used method for solving minimum-cost flow problems. However, the conventional sequential algorithms cannot satisfy the requirement of high-computational efficiency for large-scale networks. Parallel computing has resulted in numerous significant advances in science and technology over the past decades and is potential to develop an effective means to solve the computational bottleneck problem of large-scale networks. This paper first analyzes the parallelizability of network simplex algorithm and then presents a multi-granularity parallel network simplex algorithm (MPNSA) with fine- and coarse-granularity parallel strategies, which are suitable for shared- and distributed-memory parallel applications, respectively. MPNSA is achieved by message-passing interface, open multiprocessing, and compute unified device architecture, so that it can be compatible with different high-performance computing platforms. Experimental results demonstrated that MPNSA has very great accelerating effects and the maximum speedup reaches 18.7.

中文翻译：

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最小代价流问题的多粒度混合并行网络单纯形算法

最小成本流问题广泛存在于图论、计算机科学、信息科学和交通科学中。网络单纯形算法是求解最小成本流问题的一种快速且常用的方法。然而，传统的序列算法不能满足大规模网络对高计算效率的要求。在过去的几十年里，并行计算在科学和技术方面取得了许多重大进展，并且有可能开发出一种有效的手段来解决大规模网络的计算瓶颈问题。本文首先分析了网络单纯形算法的可并行性，然后提出了一种具有细粒度和粗粒度并行策略的多粒度并行网络单纯形算法（MPNSA），它们分别适用于共享和分布式内存并行应用程序。MPNSA通过消息传递接口、开放的多处理、计算统一的设备架构来实现，可以兼容不同的高性能计算平台。实验结果表明，MPNSA 具有非常大的加速效果，最大加速比达到 18.7。