A "Generalized k-Tree-Based Model to Sub-system Allocation" for Partitionable Multi-dimensional Mesh-Connected Architectures

This paper presents a new processor allocation approach called “a generalized k-Tree-based model” to perform dynamic sub-system allocation/deallocation decision for partitionable multi-dimensional mesh-connected architectures. Time complexity of our generalized k-tree-based sub-system allocation algorithm is O(k42k(NA+NF)+k 2) for the partitionable k-D meshes and O(NA+NF) for the partitionable 2-D meshes, where NA is the maximum number of allocated tasks, NF is the corresponding number of free sub-meshes, N is the system size, and NA+NF £ N. Most existing processor allocation strategies have been proposed for the partitionable 2-D meshes with various degrees of time complexity and system performance. In order to evaluate the system performance, the generalized k-Tree-based model was developed and by simulation studies the results of applying our k-Tree-based approach for the partitionable 2-D meshes were presented and compared to existing 2-D mesh-based strategies. Our results showed that the k-Tree-based approach (when it was applied for the partitionable 2-D meshes) yielded the comparable system performance to those recently 2-D mesh-based strategies.