Recursive-Parallel Algorithm for Solving the Maximum Common Subgraph Problem

Abstract

In this paper, we propose an algorithm for solving the maximum common subgraph problem. The sequential and parallel versions of the algorithm and their software implementation are described, and their effectiveness is experimentally studied. This problem is one of the most famous NP-complete problems. Its solution may be required when solving many practical problems related to the study of complex structures. We solve it in a formulation in which we need to find all possible isomorphisms of the found common subgraph. Due to the extremely high complexity of the problem, the desire to speed up its solution by parallelizing the algorithm is quite natural. To organize parallel computing, the RPM_ParLib library is used, which makes it possible to create parallel applications running on a local computer network under the control of the .NET Framework runtime environment. The library supports a recursive-parallel programming style and ensures efficient distribution of work and dynamic load balancing of computing modules during program execution. It can be used for applications written in any programming language supported by the .NET Framework. The purpose of the numerical experiment is to study the acceleration achieved through the recursive-parallel organization of calculations. For the experiment, a special application in C# that is designed to generate various sets of initial data with specified parameters is developed. Here, we describe the characteristics of the generated initial graph pairs and the results obtained during the experiment.