Partition of Random Items: Tradeoff between Binning Utility and Meta Information Leakage

In this paper, we propose a novel formulation to understand the tradeoff between binning utility and meta information leakage when we face the problems of partitioning random items. As an example, such problems could emerge when online users attempt to protect their browsing behavior patterns to certain extent by resorting to multiple proxy websites. Under the framework, we formulate a constrained optimization problem where the goal is to maximize binning utility while restraining a certain level of information leakage by properly dividing a set of M random items into N bins. By doing so, we formulate a new multi-agent multivariate optimization problem which is NP-complicated. We then utilize the submodular nature of the problem to find sufficient conditions to (1) secure the existence of a solution to our problem; (2) lower the complexity of the problem at the cost of accuracy. To do so, we exploit the dual nature of set functions in multi-agent multi-variate problems, a novel addition to the field. After proving sufficient conditions to secure the existence of a solution in more general cases, we offer algorithms and complexity orders to solve a simplified version of the problem where N=2 which helps signify the use of submodular properties.