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Multi-granularity hybrid parallel network simplex algorithm for minimum-cost flow problems

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Abstract

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.

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Acknowledgements

This work was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDA19030301); the National Natural Science Foundation of China (No. 41701452 and 41974006); the Natural Science Foundation of Guangdong (No. 2019A1515011501); and the Shenzhen Scientific Research and Development Funding Program (No. KQJSCX20180328093453763, JCYJ20180305125101282).

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  1. Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China

    Jincheng Jiang & Jinsong Chen

  2. Shenzhen Key Laboratory of Spatial Smart Sensing and Service, Research Institute for Smart Cities, School of Architecture and Urban Planning, Shenzhen University, Shenzhen, 518060, China

    Chisheng Wang

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Jiang, J., Chen, J. & Wang, C. Multi-granularity hybrid parallel network simplex algorithm for minimum-cost flow problems. J Supercomput 76, 9800–9826 (2020). https://doi.org/10.1007/s11227-020-03227-9

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