Pre-scheduling on the domain of integers

A preschedule is a static schedule without assuming constant and completely predictable rate of resource supply. A generalized prescheduling framework and a sound, complete, and PTIME preschedule generator was proposed in Wang et al. (2004) based on linear programming (LP). Since infinitely small time slices are not implementable for resources with context switch overhead, it is desirable to define and solve the prescheduling problem on the domain of integers so that context switching can occur only at boundaries of time quantums. However, integral LP (ILP) is NP-hard in the strong sense in general, so the ILP approach is not applicable and better techniques are needed. This paper answers this challenge by giving a sound, complete and PTIME rational-to-integral preschedule transformer based on a technique which we call "round-and-compensate".