Optimal Phase Barrier Synchronization in K-ary N-cube Wormhole-routed Systems Using Multirendezvous Primitives

We propose a new multiphase barrier synchronization algorithm for k-ary n-cube networks using our earlier developed multirendezvous synchronization primitives 4]. The algorithm incurs minimal cost with optimal number of communication phases. The optimality is guided by system connguration parameters (k; n) and technological parameters t s (communication start-up cost) and t p (link-propagation cost). It is shown that with moderately large n and small (t s =t p), it is possible to implement fast barrier synchronization for large number of processors with an overhead of n(t s + (k ? 1)t p). For example, with n = 6, k = 16, t p = 1, and t s = 4, it is possible to barrier synchronize 2 24 processors in 114 time units. The analysis provides a framework to determine cost-eeectiveness of implementing computations of diierent granularities on present and future wormhole-routed systems with varying system and technological parameters.