Models and Algorithms for Graph Watermarking
This work addresses the problem of protecting intellectual property in graph-structured data, which is incremental as it builds on existing watermarking concepts applied to new data types.
The paper tackles the problem of graph watermarking by introducing security definitions and feasibility characterizations, demonstrating exemplary schemes for Erdős-Rényi and random power-law graph models.
We introduce models and algorithmic foundations for graph watermarking. Our frameworks include security definitions and proofs, as well as characterizations when graph watermarking is algorithmically feasible, in spite of the fact that the general problem is NP-complete by simple reductions from the subgraph isomorphism or graph edit distance problems. In the digital watermarking of many types of files, an implicit step in the recovery of a watermark is the mapping of individual pieces of data, such as image pixels or movie frames, from one object to another. In graphs, this step corresponds to approximately matching vertices of one graph to another based on graph invariants such as vertex degree. Our approach is based on characterizing the feasibility of graph watermarking in terms of keygen, marking, and identification functions defined over graph families with known distributions. We demonstrate the strength of this approach with exemplary watermarking schemes for two random graph models, the classic Erdős-Rényi model and a random power-law graph model, both of which are used to model real-world networks.