Efficient Processor Allocation Scheme with Task Embedding for Partitionable Mesh Architectures

For partitionable Mesh architectures, a modified QT (Quad Tree)-based processor allocation scheme (MQT) with two new task embedding heuristics is proposed. Existing processor allocation strategies assume any incoming request is also represented as a mesh. This paper introduces flexibility with which the requested task can be a linear array, a ring, or a mesh and still be allocated into a partitionable Mesh network architecture. In particular, two task embedding heuristics are proposed for embedding a requested k-PE task into an “m X k/m” mesh sub-system in O(√k) time: 1) the first one is called the FS (First Size) task embedding heuristic, where m ≅ #rows of the first available sub-partition in the QT and 2) the BS (Best Size) task embedding heuristic, where embedded row = m ≅ √k and embedded column = k/m such that | m k/m | is minimum. For task embedding, the time complexity of this modified QTbased processor allocation is only O(n) if n > √k; otherwise it is O(√k), where n is the number of allocated tasks and k is the number of PEs needed. In simulation experiments, static (allocation) and dynamic (allocation and deallocation) system performances of these two modified QT-based task embedding heuristics are investigated and compared with the QT-based processor allocation with no task embedding.