Watermarking graph partitioning solutions

The authors introduce an Intellectual Property Protection (IPP) technique for graph partitioning which watermarks solutions to the graph partitioning problems so that they carry an author´s signature. This technique is completely transparent to the actual computer-aided design tool which does the partitioning and is implemented by preprocessing and postprocessing alone. The authors propose five different schemes for the watermarking of partitioning solutions. The goal is to construct a partitioning solution which not only has a small edge cut, but also encodes the signature of the author. The key idea of all of our schemes is to map the signature into a set of constraints and then satisfy a disproportionate number of these constraints. Four of our schemes are based upon the idea of encouraging groups of vertices to be in the same partition. The fifth is based upon the encouragement of certain edges to be cut by the partitioning. The fifth scheme shows superior performances on all of the cases which we tested, including both two-way and multiway partitioning. The watermarking scheme produces solutions that have very low-quality degradation levels, yet carry signatures that are convincingly unambiguous, extremely unlikely to be present by coincidence and difficult to detect or remove without completely resolving the partitioning problem.