A mathematical programming method for constructing the shortest interconnection VLSI arrays

Mesh-connected processor array is an extensively investigated architecture in parallel processing. Massive studies have addressed the problem of using reconfiguration algorithms to solve the fault tolerance of faulty mesh-connected processor arrays. However, the subarrays generated by the previous studies still contain large interconnection length, which will lead to the increase of capacitance, power dissipation and dynamic communication cost. First, a mathematical model is established for the array reconfiguration. Then, the proposed method treats the interconnections between each PEs as a function with different integer variables, which can be solved by using effective integer programming techniques. Finally, an effective solver is called to find the optimal solution. Simulation results show that the proposed method can reduce the interconnection length of the array in the row and column directions simultaneously, thereby generating a subarray with the shortest interconnection length. On a 32 x 32 host array with fault density of 30%, the total interconnection length of the subarray can be reduced by 8.36% compared with state-of-the-art, and the average interconnection length can be reduced by 39.30%, which is more closer to the lower bound.