Real-time scheduling to minimize machine busy times

Abstract

ABSTRACT.We consider the following fundamental scheduling problem. The input consists of n jobs to be scheduled on a set of machines of bounded capacities. Each job is associated with a release time, a due date, a processing time and demand for machine capacity. The goal is to schedule all of the jobs non-preemptively in their release-time-deadline windows, subject to machine capacity constraints, such that the total busy time of the machines is minimized. Our problem has important applications in power-aware scheduling, optical network design and customer service systems. Scheduling to minimize busy times is APX-hard already in the special case where all jobs have the same (unit) processing times and can be scheduled in a fixed time interval. Our main result is a 5-approximation algorithm for general instances. We extend this result to obtain an algorithm with the same approximation ratio for the problem of scheduling moldable jobs, that requires also to determine, for each job, one of several processing-time vs. demand configurations. Better bounds and exact algorithms are derived for several special cases, including proper interval graphs, intervals forming a clique and laminar families of intervals. * Work partially supported by funding for DIMACS visitors.

Scheduling maintenance jobs in networks

“…Thus, the results of Khandekar et al [14] and Chang, Khuller and Mukherjee [7] have direct implications for us. They show that minimizing busy time can be done efficiently for purely non-preemptive and purely preemptive instances, respectively.…”

“…We know that both the non-preemptive and preemptive MAXCONNECTIVITY and MINCONNECTIVITY on a path are solvable in polynomial time by Theorem 1 and [14, Theorem 9], respectively. Notice that the parameter g in [14] is in our setting ∞. Interestingly, the complexity changes when mixing the two job types -even on a simple path.…”

“…On paths, we show that mixed instances, which have both preemptive and non-preemptive jobs, are weakly NP-hard (Theorem 9). This hardness result is of particular interest, as both purely non-preemptive and purely preemptive instances can be solved efficiently on a path (see Theorem 1 and [14]). Furthermore, we give a simple 2-approximation algorithm for mixed instances of MINCONNECTIVITY (Theorem 10).…”

“…Such problems have applications for instance in the context of energy management [16] or fiber management in optical networks [11]. They have been studied from the complexity and approximation point of view in [7,11,14,16]. The problem of minimizing the busy time is equivalent to our problem in the case of a path, because there we have connectivity at a time point when no edge in the path is maintained, i. e., no machine is busy.…”

Combinatorial algorithms for scheduling jobs to minimize server usage time

“…This is why we study the Flexible Job Scheduling problem, which can be seen as a special case of the generalized MinUsageTime DBP problem by assuming the bin to have an infinite capacity. Khandekar et al [45] showed that the Flexible Job Scheduling problem can be solved in polynomial time via the dynamic programming technique in the offline setting. We thus mainly focus on the problem in the online setting in this chapter.…”