Brief Announcement: Approximation Algorithms for Preemptive Resource Allocation.

Cloud services require the allocation of scarce resources to multiple user requests (jobs) in a setting that facilitates preemption and migration while respecting resource and timing constraints. This gives rise to the following variants of the classical \em resource allocation problem (RAP). The input is a set J of jobs and a set M of homogeneous hosts, each has available amount of some resource. A job is associated with a release time, a due date, a weight and a given length, as well as its resource requirement. A feasible schedule is an allocation of the resource to a subset of the jobs, satisfying the job release times/due dates as well as the resource constraints. We consider two essential objectives: \em throughput maximization (MaxT), which seeks a maximum weight subset of the jobs that can be feasibly scheduled on the hosts in M , and \em resource minimization (MinM), that is finding the minimum number of (homogeneous) hosts needed to feasibly schedule all jobs. Both problems are known to be NP-hard. We address these fundamental problems, which have been studied previously in the \em non-preemptive model, and develop novel techniques for tackling them. In the full version of the paper, we present an $Ømega(1)$-approximation algorithm for MaxT, assuming there is sufficient slack for each job to be completed in its time window. For MinM, we study a more general setting with d resources and derive an $O(łog d)$-approximation for any fixed $d \geq 1$, under the assumption that time windows are not too small. This assumption can be removed, leading to a slightly worse ratio of $O(łog dłog^* T)$, where T is the maximum due date of any job.