Watermarking integer linear programming solutions

Linear programming (LP) in its many forms has proven to be an indispensable tool for expressing and solving optimization problems in numerous domains. We propose the first set of generic watermarking techniques for integer-LP (ILP). The proof of authorship by watermarking is achieved by introducing additional constraints to limit the solution space and can be used as effective means of intellectual property protection (IPP) and authentication. We classify and analyze the types of constraints in the ILP watermarking domain and show how ILP formulations provide more degrees of freedom for embedding signatures than other existing approaches. To demonstrate the effectiveness of the proposed ILP watermarking techniques, the generic discussion is further concretized using two examples, namely satisfiability and scheduling.