A Perfect Load Balancing Algorithm on Cube-Connected Cycles

A simple yet efficient algorithm was presented by Jan and Huang recently to distribute loads evenly on multiprocessor computers with hypercube interconnection networks. That algorithm was developed based on the well-known dimension exchange method. However, the error accumulation suffered by other algorithms based on the dimension exchange method is avoided by exploiting the notion of regular distributions, which are commonly deployed for data distributions in parallel programming. The cube-connected cycles (CCC) proposed by Preparata and Vuillemin are very similar in structure to the hypercube as an efficient general-purpose parallel system for its fixed-degree, and compact and regular layout. In this article, we propose a simple algorithm based on our previous work to distribute loads evenly on cube-connected cycles. This algorithm achieves perfect load balance over P processors with error of 1 and the worst-case time complexity of 2 ( log ) M P  , where M is the maximum load assigned to each processor initially. More importantly, it could achieve perfect load balance over subcubes as well -.if the cube is decomposed into two subcubes by bit 0, then the difference between the numbers of the total tasks in the subcubes is at most 1. Key-Words: multiprocessor, hypercube, interconnection network, cube-connected cycles, load balancing, parallel programming