Abstract

The paper proposes a parallel algorithm for solving the graph-subgraph isomorphism problem and makes an experimental study of its efficiency. The problem is one of the most well-known NP-complete problems. Its solution may be required when solving many practical problems associated with the study of complex structures. We solve the problem in a formulation that requires finding all the existing isomorphic substitutions or proving their absence. Due to the complexity of the problem, it is natural to want to speed up its solution by parallelizing the algorithm. We use the RPM_ParLib library, developed by the author, as the main tool to program the algorithm. This library allows us to develop effective applications for parallel computing on a local network under the control of the runtime environment .NET Framework. Due to this library, the applications have the ability to generate parallel branches of computation directly during program execution and dynamically redistribute work between computing modules. Any language with support of the .NET Framework can be used as a programming language in conjunction with this library. For the numerical experiment, an open database from the Internet was used, which was specially developed to study algorithms for searching for isomorphic substitutions. The author has also developed a special application in C# for generating additional sets of initial data with the specified characteristics. The aim of the experiment is to study the speedup achieved due to the recursively parallel organization of computations. This paper provides a detailed description of the proposed algorithm and the results obtained during the experiment.

中文翻译：

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求解图子图同构问题的递归并行算法

摘要

提出一种求解图子图同构问题的并行算法，并对其效率进行了实验研究。该问题是最著名的 NP 完全问题之一。在解决与复杂结构研究相关的许多实际问题时，可能需要它的解决方案。我们用一个需要找到所有现有同构替代或证明它们不存在的公式来解决问题。由于问题的复杂性，自然希望通过并行化算法来加快其求解速度。我们使用作者开发的RPM_ParLib库作为算法编程的主要工具。该库允许我们在运行时环境 .NET Framework 的控制下开发有效的应用程序，用于本地网络上的并行计算。由于这个库，应用程序能够在程序执行期间直接生成并行计算分支，并在计算模块之间动态地重新分配工作。任何支持 .NET Framework 的语言都可以用作与该库结合的编程语言。在数值实验中，使用了一个来自互联网的开放数据库，该数据库是专门为研究同构替换搜索算法而开发的。作者还用 C# 开发了一个特殊的应用程序，用于生成具有指定特征的附加初始数据集。该实验的目的是研究由于计算的递归并行组织而实现的加速。本文详细描述了所提出的算法以及实验过程中获得的结果。