Scather: programming with multi-party computation and MapReduce

We present a prototype of a distributed computational infrastructure, an associated high level programming language, and an underlying formal framework that allow multiple parties to leverage their own cloud-based computational resources (capable of supporting MapReduce [27] operations) in concert with multi-party computation (MPC) to execute statistical analysis algorithms that have privacy-preserving properties. Our architecture allows a data analyst unfamiliar with MPC to: (1) author an analysis algorithm that is agnostic with regard to data privacy policies, (2) to use an automated process to derive algorithm implementation variants that have different privacy and performance properties, and (3) to compile those implementation variants so that they can be deployed on an infrastructures that allows computations to take place locally within each participant’s MapReduce cluster as well as across all the participants’ clusters using an MPC protocol. We describe implementation details of the architecture, discuss and demonstrate how the formal framework enables the exploration of tradeoffs between the efficiency and privacy properties of an analysis algorithm, and present two example applications that illustrate how such an infrastructure can be utilized in practice.This work was supported in part by NSF Grants: #1430145, #1414119, #1347522, and #1012798

Scheduling for a Processor Sharing System with Linear Slowdown

We consider the problem of scheduling arrivals to a congestion system with a finite number of users having identical deterministic demand sizes. The congestion is of the processor sharing type in the sense that all users in the system at any given time are served simultaneously. However, in contrast to classical processor sharing congestion models, the processing slowdown is proportional to the number of users in the system at any time. That is, the rate of service experienced by all users is linearly decreasing with the number of users. For each user there is an ideal departure time (due date). A centralized scheduling goal is then to select arrival times so as to minimize the total penalty due to deviations from ideal times weighted with sojourn times. Each deviation is assumed quadratic, or more generally convex. But due to the dynamics of the system, the scheduling objective function is non-convex. Specifically, the system objective function is a non-smooth piecewise convex function. Nevertheless, we are able to leverage the structure of the problem to derive an algorithm that finds the global optimum in a (large but) finite number of steps, each involving the solution of a constrained convex program. Further, we put forward several heuristics. The first is the traversal of neighbouring constrained convex programming problems, that is guaranteed to reach a local minimum of the centralized problem. This is a form of a "local search", where we use the problem structure in a novel manner. The second is a one-coordinate "global search", used in coordinate pivot iteration. We then merge these two heuristics into a unified "local-global" heuristic, and numerically illustrate the effectiveness of this heuristic