Linear Relaxation Techniques for Task Management in Uncertain Settings

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In this paper, we consider the problem of assisting a busy user in managing her workload of pending tasks. We assume that our user is typically oversubscribed, and is invariably juggling multiple concurrent streams of tasks (or work flows) of varying importance and urgency. There is uncertainty with respect to the duration of a pending task as well as the amount of follow-on work that may be generated as a result of executing the task. The user's goal is to be as productive as possible; i.e., to execute tasks that realize the maximum cumulative payoff. This is achieved by enabling the assistant to provide advice about where and how to shed load when all tasks cannot be done. A simple temporal problem with uncertainty and preferences (called an STPPU) provides a natural framework for representing the user's current set of tasks. However, current STPPU solution techniques are inadequate as a basis for generating advice in this context, since they are applicable only in the restrictive case where all pending tasks can be accomplished within time constraints and our principal concern is support in oversubscribed circumstances. We present two techniques that are based on linear relaxation for solving the this oversubscribed problem. Given an ordering of tasks, these algorithms identify which tasks to ignore, which to compress and by how much, to maximize quality. We show experimentally that our approaches perform significantly better than techniques adapted from prior research in oversubscribed scheduling.