Abstract
We consider the problem of allocating resources for completing a collection of jobs. Each resource is specified by a start-time, finish-time and the capacity of resource available and has an associated cost, and each job is specified by a start-time, finish-time and the amount of the resource required (demand) during this interval. A feasible solution is a multiset of resources (i.e., multiple units of each resource may be picked) such that at any point of time, the sum of the capacities offered by the resources is at least the total demand of the jobs active at that point of time. The cost of the solution is the sum of the costs of the resources included in the solution (taking into account the units of the resources). The goal is to find a feasible solution of minimum cost. This problem arises naturally in many scenarios. For example, given a set of jobs, we would like to allocate some resource such as machines, memory or bandwidth in order to complete all the jobs. This problem generalizes a covering version of the knapsack problem which is known to be NP-hard. We present a constant factor approximation algorithm for this problem based on a Primal-Dual approach.