Reusable Resource Scheduling via Colored Interval Covering

Abstract

Motivated by scheduling scenarios in large shared computing systems, we study the problem of reusable resource scheduling. In this problem, there are many resources, each specified by a capacity, duration, per-use cost, and an availability window comprising of a release time and a deadline. A resources can be reused multiple times within its availability window with each use being limited by the duration associated with the resource and incurring cost equal to per-use cost. Different uses of a resource have to be non-overlapping. Given a demand profile, the goal is tocover it by scheduling the resources within their availability windows while minimizing their total cost. Reusable resource scheduling is a generalization of the well known interval covering problem. We present approximation algorithms and hardness results for the reusable resource scheduling problem. While the interval cover problem is NP-hard, it can be solved optimally for the special case where all the resources have unit capacities. In contrast, we show that the reusable resource scheduling is NP-hard and APX-hard, even for the case where the resources have unit capacities and unit costs. The approximation algorithms are derived by considering the notion of colored interval coloring, which could be of independent interest.