Certifying Induced Subgraphs in Large Graphs

TL;DR

This paper presents I/O-efficient certifying algorithms for recognizing specific graph classes, providing certificates for membership or non-membership with optimal input/output complexity, and includes practical implementations and experiments.

Contribution

It introduces the first I/O-optimal certifying algorithms for several graph classes, with implementations and experimental validation.

Findings

Algorithms operate in optimal I/O complexity.

Certificates effectively characterize class membership.

Experimental results demonstrate practical efficiency.

Abstract

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 $O(\text{sort}(n + m))$ 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.