Optimal scheduling of contract algorithms with soft deadlines

Abstract

A contract algorithm is an algorithm which is given, as part of its input, a specified amount of allowable computation time, and may not return useful results if interrupted prior to that time. In contrast, an interruptible algorithm will always output some meaningful (albeit suboptimal) solution, even if interrupted during its execution. Simulating interruptible algorithms by means of schedules of executions of contract algorithms in parallel processors is a well-studied problem with significant applications in AI. In the standard model, the interruptions are hard deadlines in which a solution must be reported immediately at the time the interruption occurs. In this paper, we study the more general setting of scheduling contract algorithms in the presence of soft deadlines. In particular, we address the setting in which if an interruption occurs at time t, then the system is given an additional window of time $w(t)\le c \cdot t$, for constant c, within which the simulation must be completed. We formulate extensions to performance measures of schedules under this setting and derive schedules of optimal performance for all concave functions w.