Incorporating Error Recovery into the Imprecise Computation Model

In this paper, we describe optimal algorithms for incorporating error recovery in the imprecise computation model. In that model each task comprises a mandatory and an optional part. The mandatory part must be completed within the task's deadline even in the presence of faults and a reward function is associated with the execution of each optional part. We address the problem of optimal scheduling in an imprecise computation environment so as to maximize total reward while simultaneously guaranteeing timely completion of recovery operations when faults occur. Furthermore, in order to prevent run-time overhead we enforce that no changes in the optimal schedule should be necessary as long as no error is detected in mandatory parts. Independent imprecise computation tasks as well as tasks with an end-to-end deadline and linear precedence constraints are considered. We present polynomial-time optimal algorithms for models with upper and lower bounds on execution times of the optional parts and for reward functions represented by general nondecreasing linear and concave functions.