Memory limited algorithms for optimal task scheduling on parallel systems

• Solves the multi-processor task scheduling problem with communication delays.
• Two new memory limited optimal task scheduling algorithms are proposed.
• Their implementations have a small memory footprint.
• Complimentary approach to the optimal solution, from below and above.
• Computes non-optimal but quality guaranteed solutions on request.

To fully benefit from a multi-processor system, tasks need to be scheduled optimally. Given that the task scheduling problem with communication delays, P|prec,cij|CmaxP|prec,cij|Cmax, is a well known strong NP-hard problem, exhaustive approaches are necessary. The previously proposed A* based algorithm retains its entire state space in memory and often runs out of memory before it finds an optimal solution. This paper investigates and proposes two memory limited optimal scheduling algorithms: Iterative Deepening A* (IDA*) and Depth-First Branch and Bound A* (BBA*). When finding a guaranteed near optimal schedule length is sufficient, the proposed algorithms can be combined, reporting the gap while they run. Problem specific pruning techniques, which are crucial for good performance, are studied for the two proposed algorithms. Extensive experiments are conducted to evaluate and compare the proposed algorithms with previous optimal algorithms.