An Approach to Graph Matching in the Component of Model Transformations

Abstract

-Nowadays approaches, based on models, are used in the development of the information systems. The models can be changed during the system development process by developers. They can be transformed automatically: visual model can be translated into program code; transformation from one modeling language to other can be done. The most appropriate way of the formal visual model presentation is metagraph. The best way to describe changes of visual models is the approach, based on graph grammars (graph rewriting). It is the most demonstrative way to present the transformation. But applying the graph grammar to the graph of model means to find the subgraph isomorphic to the left part of the grammar rule. This is an NP-complete task. There are some algorithms, developed for solving this task. They were designed for ordinary graphs and hypergraphs. In this article we consider some of them in case of using with the metagraphs representing models.

A Multilayer Approach to Subgraph Matching in HP-graphs

“…The problem of subgraph matching has been investigated for many years. The works of many scientists, such as [16]- [18], are dedicated to exploring applicability, time complexity and limitations of the existing subgraph matching algorithms. These algorithms are generally divided into two classes:…”

“…CFL-Match [24] present all candidates as a CPI-structure, where all the pattern embeddings are filtered and validated by traversing this tree structure. The most of theoretical research of this problem was conducted specifically for ordinary graphs [18]; that is why the approaches of these algorithms have to be adapted to an HP-graph model. In particular, this paper presents an adaptation of a standard backtracking algorithm for subgraph matching, the Ullmann algorithm [19] and the VF2 algorithm [20], which are optimized for the multilayer structure of this graph model.…”