Using the duplicaticity of a taskgraph to select a suitable multiprocessor scheduling strategy

Most multiprocessor taskgraph scheduling algorithms are variations of the priority list scheduling approach where interprocessor communication-overheads are ignored. An alternative is duplication-based scheduling, where tasks are duplicated on multiple processors to reduce inter-processor traffic. However, these strategies are more suitable for taskgraphs with a certain structure exhibiting a high degree of fan-out. Therefore, not all taskgraphs can be scheduled efficiently using duplication. In this paper a new and easily computed measure is introduced the degree of duplicaticity. The degree of duplicaticity quantifies the suitability of applying a duplication-based strategy to a taskgraph, and it can thus be used as an indicator for deciding weather to employ a traditional list-scheduling technique or a duplication based technique. 1 Task graph scheduling The NP hard multiprocessor static taskgraph scheduling problem have received sustained attention for several decades. It involves assigning the vertices, or tasks, of an acyclic directed graph onto a set of interconnected processing elements such that the makespan, or total computing time, is minimised. Most approaches belong to the family of prioritylist scheduling algorithms, differentiated by the way in which task priorities are assigned. There is a large number of strategies that are easy to implement and that produce powerful results, for example demand scheduling, critical-path [1], highest level first known execution times (HLFET), shortest co-level first known execution times (SCEFT), graphlevel/communication intensity, Dynamic Highest Level First/Most Immediate Successor First (DHLF/MISF), Depth First/Heuristics (DF/H), Depth First/Implicit Heuristic Search (DF/IHS) [2, 3, 4] and the famous and frequently cited Critical Path/Most Immediate Successor First (CP/MISF) [5] proposed by Kasahara and Narita. There are also more complex and harder-to-implement strategies that produce marginally better results, for example dynamic critical path scheduling [6]. More recently, researchers have employed modern stochastic search techniques, such as evolutionary strategies, to obtain better schedules. The most cited approach was proposed by Ahmad and Dhodhi who generated close-to-optimal schedules by combing the traditional CP/MISF approach with an evolutionary search strategy [7], and variations on the theme has been carried