Graph and subgraph isomorphism and their applications
Graph and subgraph isomorphism and their applications
Some applications of graph and subgraph isomorphism are discussed, particular consideration being given to the graph representations used. Graph isomorphism of very large graphs (up to 1000 vertices) is considered. A novel implementation of a modified form of the Corneal isomorphism algorithm is developed, having approximately 0(nlogn) time dependence for random graphs. A recursive form of the Corneil algorithm, not dependent upon a conjecture, is also developed. The algorithm is still inefficient for certain classes of regular graphs. A depth first search technique is developed to perform subgraph isomorphism of small graphs into large graphs. The use of various refinement procedures reduces the number of successor nodes in the tree search. Significant improvements in run time over existing algorithms are achieved. Techniques for representing a relationship between more than two vertices of a graph are considered. The concept of a device is developed, and is implemented using an edge labelling scheme, or by hyperedges. Heirarchical structures may be represented by these nested devices. The subgraph algorithm is extended to allow isomorphism tests between these heirarchical hypergraphs.
University of Southampton
1981
Crowhurst, Peter Dennis
(1981)
Graph and subgraph isomorphism and their applications.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
Some applications of graph and subgraph isomorphism are discussed, particular consideration being given to the graph representations used. Graph isomorphism of very large graphs (up to 1000 vertices) is considered. A novel implementation of a modified form of the Corneal isomorphism algorithm is developed, having approximately 0(nlogn) time dependence for random graphs. A recursive form of the Corneil algorithm, not dependent upon a conjecture, is also developed. The algorithm is still inefficient for certain classes of regular graphs. A depth first search technique is developed to perform subgraph isomorphism of small graphs into large graphs. The use of various refinement procedures reduces the number of successor nodes in the tree search. Significant improvements in run time over existing algorithms are achieved. Techniques for representing a relationship between more than two vertices of a graph are considered. The concept of a device is developed, and is implemented using an edge labelling scheme, or by hyperedges. Heirarchical structures may be represented by these nested devices. The subgraph algorithm is extended to allow isomorphism tests between these heirarchical hypergraphs.
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Published date: 1981
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Local EPrints ID: 460549
URI: http://eprints.soton.ac.uk/id/eprint/460549
PURE UUID: 80fc6e75-7eca-46ba-a0cb-4f96d08c7151
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Date deposited: 04 Jul 2022 18:24
Last modified: 04 Jul 2022 18:24
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Author:
Peter Dennis Crowhurst
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