Efficient subtorus processor allocation in a multi-dimensional torus

Processor allocation in a mesh or torus connected multicomputer system with up to three dimensions is a hard problem that has received some research attention in the past decade. With the recent deployment of multicomputer systems with a torus topology of dimensions higher than three, which are used to solve complex problems arising in scientific computing, it becomes imminent to study the problem of allocating processors of the configuration of a torus in a multi-dimensional torus connected system. In this paper, we first define the concept of a semitorus. We present two partition schemes, the Equal Partition (EP) and the Non-Equal Partition (NEP), that partition a multi-dimensional semitorus into a set of sub-semitori. We then propose two processor allocation algorithms based on these partition schemes. We evaluate our algorithms by incorporating them in commonly used FCFS and backfilling scheduling policies and conducting simulation using workload traces from the Parallel Workloads Archive. Specifically, our simulation experiments compare four algorithm combinations, FCFS/EP, FCFS/NEP, backfilling/EP, and backfilling/NEP, for two existing multi-dimensional torus connected systems. The simulation results show that our algorithms (especially the backfilling/NEP combination) are capable of producing schedules with system utilization and mean job bounded slowdowns comparable to those in a fully connected multicomputer.