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Within a given collection of graphs, a graph retrieval system may seek all graphs that contain a given graph, or may instead seek all graphs that are contained within a given graph. Although subgraph isomorphism is worst-case exponential, it may be average-case polynomial if graphs are labeled so as to restrict possible correspondences between vertices of included and includer graphs. Degree reduction is a procedure that uses logical inference to preclude some such correspondences, thereby substantially increasing the size of includer graphs that can be processed, without preventing any existent isomorphism from being found. Degree reduction works only with labeled graphs, which may be directed or undirected, with or without edge labels. Inexact or approximate isomorphism is accommodated by reducing strictness of conditions for perfect isomorphism. Disk-based degree reduction, which is an order of magnitude slower than memory-based degree reduction, has successfully processed graphs that have millions of vertices. Although the principle of degree reduction is simple and fundamental, its efficient practical implementation involves intricate procedural detail. Its average-case complexity analysis is currently intractable, so cost-benefit assessment has to be experimental. [ABSTRACT FROM AUTHOR]

Within a given collection of graphs, a graph retrieval system may seek all graphs that contain a given graph, or may instead seek all graphs that are contained within a given graph. Although subgraph isomorphism is worst-case exponential, it may be average-case polynomial if graphs are labeled so as to restrict possible correspondences between vertices of included and includer graphs. Degree reduction is a procedure that uses logical inference to preclude some such correspondences, thereby substantially increasing the size of includer graphs that can be processed, without preventing any existent isomorphism from being found. Degree reduction works only with labeled graphs, which may be directed or undirected, with or without edge labels. Inexact or approximate isomorphism is accommodated by reducing strictness of conditions for perfect isomorphism. Disk-based degree reduction, which is an order of magnitude slower than memory-based degree reduction, has successfully processed graphs that have millions of vertices. Although the principle of degree reduction is simple and fundamental, its efficient practical implementation involves intricate procedural detail. Its average-case complexity analysis is currently intractable, so cost-benefit assessment has to be experimental. [ABSTRACT FROM AUTHOR]

Within a given collection of graphs, a graph retrieval system may seek all graphs that contain a given graph, or may instead seek all graphs that are contained within a given graph. Although subgraph isomorphism is worst-case exponential, it may be average-case polynomial if graphs are labeled so as to restrict possible correspondences between vertices of included and includer graphs. Degree reduction is a procedure that uses logical inference to preclude some such correspondences, thereby substantially increasing the size of includer graphs that can be processed, without preventing any existent isomorphism from being found. Degree reduction works only with labeled graphs, which may be directed or undirected, with or without edge labels. Inexact or approximate isomorphism is accommodated by reducing strictness of conditions for perfect isomorphism. Disk-based degree reduction, which is an order of magnitude slower than memory-based degree reduction, has successfully processed graphs that have millions of vertices. Although the principle of degree reduction is simple and fundamental, its efficient practical implementation involves intricate procedural detail. Its average-case complexity analysis is currently intractable, so cost-benefit assessment has to be experimental. [ABSTRACT FROM AUTHOR]