Certifying Induced Subgraphs in Large Graphs

10/24/2022

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by   Ulrich Meyer, et al.

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We introduce I/O-optimal certifying algorithms for bipartite graphs, as well as for the classes of split, threshold, bipartite chain, and trivially perfect graphs. When the input graph is a class member, the certifying algorithm returns a certificate that characterizes this class. Otherwise, it returns a forbidden induced subgraph as a certificate for non-membership. On a graph with n vertices and m edges, our algorithms take optimal O(sort(n + m)) I/Os in the worst case or with high probability for bipartite chain graphs, and the certificates are returned in optimal I/Os. We give implementations for split and threshold graphs and provide an experimental evaluation.