Abstract
Visual modeling is widely used nowadays, but the existing modeling platforms cannot meet all the user requirements. Visual languages are usually based on graph models, but the graph types used have significant restrictions. A new graph model, called HP-graph, whose main element is a set of poles, the subsets of which are combined into vertices and edges, has been previously presented to solve the problem of insufficient expressiveness of the existing graph models. Transformations and many other operations on visual models face a problem of subgraph matching, which slows down their execution. A multilayer approach to subgraph matching can be a solution for this problem if a modeling system is based on the HP-graph. In this case, the search is started on the higher level of the graph model, where vertices and hyperedges are compared without revealing their structures, and only when a candidate is found, it moves to the level of poles, where the comparison of the decomposed structures is performed. The description of the idea of the multilayer approach is given. A backtracking algorithm based on this approach is presented. The Ullmann algorithm and VF2 are adapted to this approach and are analyzed for complexity. The proposed approach incrementally decreases the search field of the backtracking algorithm and helps to decrease its overall complexity. The paper proves that the existing subgraph matching algorithms except ones that modify a graph pattern can be successfully adapted to the proposed approach.
Highlights
The study of any objects and processes, as well as their design, can barely be done without modeling; that is why software tools that allow specialists to build various models and formalize descriptions of objects and processes, or use modeling as a method of analysis, are becoming more popular
The paper [7] proved that this graph model allows the creation of a flexible visual model editor based on it
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
Summary
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. Most of these algorithms use backtracking to move through the built search tree and find appropriate combination of corresponding vertices of the source graph and the graph-pattern Algorithms in this class include Ullmann algorithm [19], VF2 [20] (and VF2 Plus [21] and VF3 [22]), TurboISO [23], CFL-Match [24], QuickSI [25], SPath [26] and others. SPath [26] uses neighborhood signature for each vertex to store information about the surrounding vertices These signatures are compared with the corresponding signatures of the query graph and are used for search space pruning before subgraph matching.
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