On the resilience of canonical reducible permutation graphs

An ingenious graph-based watermarking scheme recently proposed by Chroni and Nikolopoulos encodes integers as a special type of reducible permutation graphs. It was claimed without proof that those graphs can withstand attacks in the form of a single edge removal. We introduce a linear-time algorithm which restores the original graph after removals of k≤2 edges, therefore proving an even stronger result. Furthermore, we prove that k≤5 general edge modifications (removals/insertions) can always be detected in polynomial time. Both bounds are tight. Our results reinforce the interest in regarding Chroni and Nikolopoulos’s scheme as a possible software watermarking solution for numerous applications.