International Journal of Combinatorics / 2012 / Article / Tab 4

Research Article

A Convex Relaxation Bound for Subgraph Isomorphism

Table 4

Summarisation of the results. We performed 1000 ( ) random subgraph experiments from which 661 ( ) instances are known to have no subgraph isomorphism. The column denoted with shows how often the bound was not tight enough to detect that no subgraph isomorphism can be found. In cases the bound is tight enough. Without preprocessing the problem matrix size is while with the described pruning the size varies from problem instance to problem instance. However the mean problem matrix is reduced to about ( ).

Preproc.K/L

Non 7/15 1000 661 123 ( 19%) 877 538
Pruning 7/15 1000 661 327 ( 49%) 673 334

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