Graph-based approaches for the interval scheduling problem

One of the fundamental problems encountered by large-scale computing systems, such as clusters and cloud, is to schedule a set of jobs submitted by the users. Each job is characterized by resource demands, as well as start and completion time. Each job must be scheduled to execute on a machine having the required capacity between the start and completion time (referred as interval) of the job. Each machine is defined by a parallelism parameter g that indicates the maximum number of jobs that can be processed by the machine, in parallel. The above problem is referred to as the interval scheduling problem with bounded parallelism. The objective is to minimize the total busy time of all machines. Majority of the solutions proposed in the literature consider homogeneous set of jobs and machines that is a simplified assumption as in practice, heterogeneous jobs and machines are frequently encountered. In this article, we tackle the aforesaid problem with a set of heterogeneous jobs and machines. A major contribution of our work is that the problem is addressed in a novel way by combining a graph-based approach and a dynamic programming approach which is based on a variation of bin packing problem. A greedy algorithm is also proposed by employing only a graph-based approach at the aim to reduce the computational complexity. Experimental results show that the proposed algorithms can significantly reduce the cumulative busy interval over all machines compared with state-of-the-art algorithms proposed in the literature.