Revisiting a BSP/CGM transitive closure algorithm

We present a new BSP/CGM parallel algorithm for the transitive closure problem. Our algorithm uses O(n³/pα) local computation time with O(p/α) communication rounds, where α is the size in bits that can be stored in a primitive data item. For all the randomly generated graphs that were used in the tests, the number of communication rounds was bounded by log p/α+1. Our algorithm, even for the worst case, improves the previous results. The algorithm was implemented and the results show the efficiency and scalability of the presented algorithm and compare favorably with other parallel implementations.