Aligning block permutation methods for topology transformation on computational grids

Abstract

Many traditional parallel matrix computing algorithms are performed on regular resource topologies, such as mesh. However, the grid resource topology is often irregular in practice. In this paper, we present a transformation algorithm of grid resource topology for achieving virtual meshes. And on the virtual mesh, these traditional parallel algorithms can be performed in a modern computational grid environment. The basic idea of our topology transformation is to align the basic blocks of grid computational resources through permutations in a virtual mesh. Designing a cost function of heuristic search scheme for the transformation, we use it to fully exploit the computational and communicational abilities of grid resources. The experiment results show that our aligning block permutation can significantly reduce the time complexity of search tree. They also show that the heuristic search scheme can effectively find the block permutation that makes better use of computational and communicational abilities of grid resources.