The paper proposes a new inference task for graphical models. It consists in finding a MAP assignment w.r.t. one distribution p such that its probability w.r.t. another distribution q is bounded. It contains as special cases several interesting graphical model problems like m-best assigments. The method uses a transformation to multiple choice knapsack for cmputationally solving the problem. Authors agree that the new problem is interesting and the transformation to multiple choice knapsack is interesting. The main criticism pertains to the small experiments that are not necessarily indicative of real-world problems. The interesting new problem formulation and innovative solution technique still merit publication at NeurIPS.