Reconfiguration algorithms for synchronous communication on switch based degradable arrays

Abstract

Synchronous communication is one of the most important issues in high performance architectures for large scale of parallel computing, such as matrix computing, image processing, etc. Mesh-connected processor array is characteristic of synchronous communication due to the same length of the interconnects between the neighboring processing elements (PEs) in rows/columns. But long interconnects caused by faulty PEs clearly impact the synchronous communication between the adjacent rows/columns. If long interconnects exist between two adjacent rows, we say that a synchronous communication delay is caused. This paper contributes algorithms to construct logical arrays with synchronous communication in a given host array. Specifically, an algorithm for synchronous communication array (ASCA) is firstly presented, to construct a maximum logical array with synchronous communication. When all of the long interconnects are independent each other, the proposed algorithm is proved to be optimal. After that, two heuristic algorithms are also proposed, to construct a logical array with given size, by integrating the proposed ASCA and two exclusion schemes. The proposed two exclusion schemes are based on strategies of divide-and-conquer and the longest logical column first, respectively. In addition, the lower bound of synchronous communication delay for a logical array is calculated by an algorithm also developed in this paper, in order to evaluate the synchronous performance of reconfiguration algorithms. Simulation results show that, the proposed two heuristic algorithms have their own advantages for different cases. The synchronous communication delay of the logical arrays is significantly reduced, and it is very close to the lower bound for the cases of small fault density and larger exclusion rate. For 32 × 32 physical arrays with exclusion rates that are larger than 15%, the synchronous communication delay of logical array is reduced from 11.09 to 6.97, which is more closer to the lower bound 4.43, for different fault densities on average.