An Algorithm for Subgraph Isomorphism

Ullmann, J. R.

doi:10.1145/321921.321925

Cited by 1,866 publications

(1,069 citation statements)

References 10 publications

Supporting

Mentioning

1,061

Contrasting

Unclassified

Order By: Relevance

“…However, as proved in [22], given a pair of graphs, it is NP-hard to determine whether they have the same structure. That means it is intractable to compare pairwise RCGs directly.…”

Section: Discriminative Structures Selectionmentioning

confidence: 99%

An aerial image recognition framework using discrimination and redundancy quality measure

Nie

2016

Journal of Visual Communication and Image Representation

View full text Add to dashboard Cite

Aerial image categorization plays an indispensable role in remote sensing and artificial intelligence. In this paper, we propose a new aerial image categorization framework, focusing on organizing the local patches of each aerial image into multiple discriminative subgraphs. The subgraphs reflect both the geometric property and the color distribution of an aerial image. First, each aerial image is decomposed into a collection of regions in terms of their color intensities. Thereby region connected graph (RCG), which models the connection between the spatial neighboring regions, is constructed to encode the spatial context of an aerial image. Second, a subgraph mining technique is adopted to discover the frequent structures in the RCGs constructed from the training aerial images. Thereafter, a set of refined structures are selected among the frequent ones toward being highly discriminative and low redundant. Lastly, given a new aerial image, its sub-RCGs corresponding to the refined structures are extracted. They are further quantized into a discriminative vector for SVM classification. Thorough experimental results validate the effectiveness of the proposed method. In addition, the visualized mined subgraphs show that the discriminative topologies of each aerial image are discovered.

show abstract

“…However, as proved in [22], given a pair of graphs, it is NP-hard to determine whether they have the same structure. That means it is intractable to compare pairwise RCGs directly.…”

Section: Discriminative Structures Selectionmentioning

confidence: 99%

An aerial image recognition framework using discrimination and redundancy quality measure

Nie

2016

Journal of Visual Communication and Image Representation

View full text Add to dashboard Cite

show abstract

“…To determine whether one graph is a subgraph of another one can apply a computational procedure known as a subgraph isomorphism algorithm. A number of such algorithms exist and studies have demonstrated the general effectiveness of the Ullmann subgraph isomorphism algorithm for searching both small molecules and biological macromolecules [32,33,21]). We have used the Ullmann algorithm as the basis for our program NASSAM.…”

Section: The Ullmann Subgraph Isomorphism Algorithmmentioning

confidence: 99%

Representation, searching and discovery of patterns of bases in complex RNA structures

Harrison

South

Willett

et al. 2003

Journal of Computer-Aided Molecular Design

View full text Add to dashboard Cite

SummaryWe describe a graph theoretic method designed to perform efficient searches for substructural patterns in nucleic acid structural coordinate databases using a simplified vectorial representation. Two vectors represent each nucleic acid base and the relative positions of bases with respect to one another are described in terms of distances between the defined start and end points of the vectors on each base. These points comprise the nodes and the distances the edges of a graph, and a pattern search can then be performed using a subgraph isomorphism algorithm.The minimal representation was designed to facilitate searches for complex patterns but was first tested on simple, well-characterised arrangements of bases such as base pairs and GNRA-tetraloop receptor interactions. The method performed very well for these interaction types. A survey of side-by-side base interactions, of which the adenosine platform is the best known example also locates examples of similar base rearrangements that we consider to be 2 important in structural regulation. A number of examples were found, with GU platforms being particularly prevalent. A GC platform in the RNA of the Thermus thermophilus small ribosomal subunit is in an analogous position to an adenosine platform in other species. An unusual GG platform is also observed close to one of the substrate binding sites in Haloarcula marismortui large ribosomal subunit RNA.Abbreviations PDB Protein Databank 3D three-dimensional GNRA Guanine, N = any base, R = pyrimidine base, Adenine 3

show abstract

“…This essentially means that instead of searching for TNFs with identical values, algorithms must ensure that TNF values from subgraph nodes are less than or equal to the corresponding TNF values from the full graph. One of the earliest and most influential subgraph isomorphism algorithms was Ullmann's algorithm [19]. Based on a tree search with backtracking, and a refinement procedure to prune the search tree, Ullmann's algorithm maintained state of the art performance until being superseded by the VF2 algorithm.…”

Section: Introductionmentioning

confidence: 99%

Efficient subgraph matching using topological node feature constraints

Dahm

Bunke

Caelli

et al. 2015

Pattern Recognition

View full text Add to dashboard Cite

a b s t r a c tThis paper presents techniques designed to minimise the number of states which are explored during subgraph isomorphism detection. A set of advanced topological node features, calculated from nneighbourhood graphs, is presented and shown to outperform existing features. Further, the pruning effectiveness of both the new and existing topological node features is significantly improved through the introduction of strengthening techniques. In addition to topological node features, these strengthening techniques can also be used to enhance application-specific node labels using a proposed novel extension to existing pruning algorithms. Through the combination of these techniques, the number of explored search states can be reduced to near-optimal levels.

show abstract

An Algorithm for Subgraph Isomorphism

Cited by 1,866 publications

References 10 publications

An aerial image recognition framework using discrimination and redundancy quality measure

An aerial image recognition framework using discrimination and redundancy quality measure

Representation, searching and discovery of patterns of bases in complex RNA structures

Efficient subgraph matching using topological node feature constraints

Contact Info

Product

Resources

About