This paper studies the design of an optimal privacyaware estimator of a public random variable based on noisy measurements which contain private information. The public random variable carries non-private information, however, its estimate will be correlated with the private information due to the estimation process. It is assumed that the estimate of the public random variable is revealed to an untrusted party. The objective is to design an estimator for the public random variable such that the leakage of the private information, via the estimation process, is kept below a certain level. The privacy metric is defined as the discrete conditional entropy of the private random variable, which carries the private information, given the output of the estimator. A binary loss function is considered for the estimation of the public random variable. It is shown that the optimal privacy-aware estimator is the solution of a (possibly infinite-dimensional) convex optimization problem. We next study the optimal perfect privacy estimator which ensures that the estimate of the public random variable is independent of the private information. A necessary and sufficient condition is derived which guarantees that an estimator satisfies the perfect privacy requirement. It is shown that the optimal perfect privacy estimator is the solution of a linear optimization problem. A sufficient condition for the existence of the optimal perfect privacy estimator is derived when the estimator has access to discretized measurements of sensors.
On the Complexity and Approximability of Budget-Constrained Minimum Cost Flows
本文研究了带约束的最小费用流问题的复杂性和可逼近性，该问题是传统最小费用流问题的一种扩展，通过引入与每条边相关的第二类费用，其在可行流中的总价值受到给定预算B的约束.这个问题可以，例如，可看作是ε-约束方法在双准则最小费用流问题中的应用。我们证明了我们可以在弱多项式时间$O(\log M \cdot MCF(m,n,C,U))$内精确地求解该问题，其中C，U和M分别是输入中出现的任意数的最大绝对费用、最大容量和最大绝对值的上界，MCF（m，n，C，U）表示寻找传统最小费用流的复杂性.此外，我们提出了两个完全多项式时间的近似计划的问题一般图和一个改进的运行时间的问题的无圈图。
A Heuristic Alternating Direction Method of Multipliers Framework for Distributed and Centralized Tree-Constrained Optimization: Applications to Hop-Constrained Spanning Tree Multicommodity Flow Design
New Jersey Institute of Technology (NJIT)（新泽西理工学院）
