Indexing with Well-Founded Total Order for Faster Subgraph Isomorphism Detection

Indexing with Well-Founded Total Order for Faster Subgraph Isomorphism Detection
Markus Weber, Marcus Liwicki, Andreas Dengel
Graph-Based Representations in Pattern Recognition: 8th IAPR-TC-15 International Workshop IAPR International Workshop on Graph-Based Representations in Pattern Recognition (GbR-11), 8th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition, May 18-20, Münster, Germany

Abstract:

In this paper an extension of index-based subgraph matching is proposed. This extension significantly reduces the storage amount and indexing time for graphs where the nodes are labeled with a rather small amount of different classes. In order to reduce the number of possible permutations, a weight function for labeled graphs is introduced and a well-founded total order is defined on the weights of the labels. Inversions which violate the order are not allowed. A computational complexity analysis of the new preprocessing is given and its completeness is proven. Furthermore, in a number of practical experiments with randomly generated graphs the improvement of the new approach is shown. In experiments performed on random sample graphs, the number of permutations has been decreased to a fraction of 10^18 in average compared to the original approach by Messmer. This makes indexing of larger graphs feasible, allowing for fast detection of subgraphs.

Keywords:

Graph isomorphism; Subgraph isomorphism; Tree search; Decision tree; Indexing