Capturing Topology in Graph Pattern Matching

Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be conducted in cubic-time. However, they fall short of capturing the topology of data graphs, i.e., graphs may have a structure drastically different from pattern graphs they match, and the matches found are often too large to understand and analyze. To rectify these problems, this paper proposes a notion of strong simulation, a revision of graph simulation, for graph pattern matching. (1) We identify a set of criteria for preserving the topology of graphs matched. We show that strong simulation preserves the topology of data graphs and finds a bounded number of matches. (2) We show that strong simulation retains the same complexity as earlier extensions of simulation, by providing a cubic-time algorithm for computing strong simulation. (3) We present the locality property of strong simulation, which allows us to effectively conduct pattern matching on distributed graphs. (4) We experimentally verify the effectiveness and efficiency of these algorithms, using real-life data and synthetic data.Comment: VLDB201

Representation and generation of plans using graph spectra

Numerical comparison of spaces with one another is often achieved with set scalar measures such as global and local integration, connectivity, etc., which capture a particular quality of the space but therefore lose much of the detail of its overall structure. More detailed methods such as graph edit distance are difficult to calculate, particularly for large plans. This paper proposes the use of the graph spectrum, or the ordered eigenvalues of a graph adjacency matrix, as a means to characterise the space as a whole. The result is a vector of high dimensionality that can be easily measured against others for detailed comparison. Several graph types are investigated, including boundary and axial representations, as are several methods for deriving the spectral vector. The effectiveness of these is evaluated using a genetic algorithm optimisation to generate plans to match a given spectrum, and evolution is seen to produce plans similar to the initial targets, even in very large search spaces. Results indicate that boundary graphs alone can capture the gross topological qualities of a space, but axial graphs are needed to indicate local relationships. Methods of scaling the spectra are investigated in relation to both global local changes to plan arrangement. For all graph types, the spectra were seen to capture local patterns of spatial arrangement even as global size is varied

Craquelure as a Graph: Application of Image Processing and Graph Neural Networks to the Description of Fracture Patterns

Cracks on a painting is not a defect but an inimitable signature of an artwork which can be used for origin examination, aging monitoring, damage identification, and even forgery detection. This work presents the development of a new methodology and corresponding toolbox for the extraction and characterization of information from an image of a craquelure pattern. The proposed approach processes craquelure network as a graph. The graph representation captures the network structure via mutual organization of junctions and fractures. Furthermore, it is invariant to any geometrical distortions. At the same time, our tool extracts the properties of each node and edge individually, which allows to characterize the pattern statistically. We illustrate benefits from the graph representation and statistical features individually using novel Graph Neural Network and hand-crafted descriptors correspondingly. However, we also show that the best performance is achieved when both techniques are merged into one framework. We perform experiments on the dataset for paintings' origin classification and demonstrate that our approach outperforms existing techniques by a large margin.Comment: Published in ICCV 2019 Workshop