Isomorphism

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Jeong Hoon Lee - One of the best experts on this subject based on the ideXlab platform.

  • An in-depth comparison of subgraph Isomorphism algorithms in graph databases
    Proceedings of the VLDB Endowment, 2012
    Co-Authors: Jinsoo Lee, Romans Kasperovics, Wook-shin Han, Jeong Hoon Lee
    Abstract:

    Finding subgraph Isomorphisms is an important problem in many applications\nwhich deal with data modeled as graphs. While this problem is NP-hard,\nin recent years, many algorithms have been proposed to solve it in\na reasonable time for real datasets using different join orders,\npruning rules, and auxiliary neighborhood information. However, since\nthey have not been empirically compared one another in most research\nwork, it is not clear whether the later work outperforms the earlier\nwork. Another problem is that reported comparisons were often done\nusing the original authors' binaries which were written in different\nprogramming environments. In this paper, we address these serious\nproblems by re-implementing five state-of-the-art subgraph Isomorphism\nalgorithms in a common code base and by comparing them using many\nreal-world datasets and their query loads. Through our in-depth analysis\nof experimental results, we report surprising empirical findings.

Yves Lecourtier - One of the best experts on this subject based on the ideXlab platform.

  • an integer linear program for substitution tolerant subgraph Isomorphism and its use for symbol spotting in technical drawings
    Pattern Recognition, 2012
    Co-Authors: Pierre Le Bodic, Pierre Heroux, Sebastien Adam, Yves Lecourtier
    Abstract:

    This paper tackles the problem of substitution-tolerant subgraph Isomorphism which is a specific class of error-tolerant Isomorphism. This problem aims at finding a subgraph Isomorphism of a pattern graph S in a target graph G. This Isomorphism only considers label substitutions and forbids vertex and edge insertion in G. This kind of subgraph Isomorphism is often needed in pattern recognition problems when graphs are attributed with real values and no exact matching can be found between attributes due to noise. Our proposal to solve the problem of substitution-tolerant subgraph Isomorphism relies on its formulation in the Integer Linear Program (ILP) formalism. Using a general ILP solver, the approach is able to find, if one exists, a mapping of a pattern graph into a target graph such that the topology of the searched graph is kept and the editing operations between the labels have a minimal cost. This technique is evaluated on both a set of synthetic graphs and a problem of symbol detection in technical drawings. In the second case, document and symbol images are represented by vector-attributed Region Adjacency Graphs built from a segmentation process. Obtained results demonstrate the relevance of considering subgraph Isomorphism as an optimization process.

Jinsoo Lee - One of the best experts on this subject based on the ideXlab platform.

  • An in-depth comparison of subgraph Isomorphism algorithms in graph databases
    Proceedings of the VLDB Endowment, 2012
    Co-Authors: Jinsoo Lee, Romans Kasperovics, Wook-shin Han, Jeong Hoon Lee
    Abstract:

    Finding subgraph Isomorphisms is an important problem in many applications\nwhich deal with data modeled as graphs. While this problem is NP-hard,\nin recent years, many algorithms have been proposed to solve it in\na reasonable time for real datasets using different join orders,\npruning rules, and auxiliary neighborhood information. However, since\nthey have not been empirically compared one another in most research\nwork, it is not clear whether the later work outperforms the earlier\nwork. Another problem is that reported comparisons were often done\nusing the original authors' binaries which were written in different\nprogramming environments. In this paper, we address these serious\nproblems by re-implementing five state-of-the-art subgraph Isomorphism\nalgorithms in a common code base and by comparing them using many\nreal-world datasets and their query loads. Through our in-depth analysis\nof experimental results, we report surprising empirical findings.

Hamid Krim - One of the best experts on this subject based on the ideXlab platform.

  • object recognition through topo geometric shape models using error tolerant subgraph Isomorphisms
    IEEE Transactions on Image Processing, 2010
    Co-Authors: Sajjad Baloch, Hamid Krim
    Abstract:

    We propose a method for 3-D shape recognition based on inexact subgraph Isomorphisms, by extracting topological and geometric properties of a shape in the form of a shape model, referred to as topo-geometric shape model (TGSM). In a nutshell, TGSM captures topological information through a rigid transformation invariant skeletal graph that is constructed in a Morse theoretic framework with distance function as the Morse function. Geometric information is then retained by analyzing the geometric profile as viewed through the distance function. Modeling the geometric profile through elastic yields a weighted skeletal representation, which leads to a complete shape signature. Shape recognition is carried out through inexact subgraph Isomorphisms by determining a sequence of graph edit operations on model graphs to establish subgraph Isomorphisms with a test graph. Test graph is recognized as a shape that yields the largest subgraph Isomorphism with minimal cost of edit operations. In this paper, we propose various cost assignments for graph edit operations for error correction that takes into account any shape variations arising from noise and measurement errors.

Peter Willett - One of the best experts on this subject based on the ideXlab platform.

  • identification of tertiary structure resemblance in proteins using a maximal common subgraph Isomorphism algorithm
    Journal of Molecular Biology, 1993
    Co-Authors: Helen M Grindley, Peter J Artymiuk, David W Rice, Peter Willett
    Abstract:

    Abstract A program called PROTEP is described that permits the rapid comparison of pairs of three-dimensional protein structures to identify the patterns of secondary structure elements that they have in common. The representation of the protein structures as labelled graphs, where the secondary structure elements in a protein and the spatial and angular relationships between them correspond to the nodes and edges of a graph, was developed for use with an earlier program, called POSSUM, which identified subgraph Isomorphisms in protein structures. PROTEP takes this representation and uses a different and more flexible approach to locating structural patterns in pairs of proteins, using a maximal common subgraph Isomorphism algorithm that is based on a clique detection procedure. A range of searches is described to demonstrate that areas of common structural overlap between protein structures taken from the Protein Data Bank can be identified both effectively and efficiently.