Optimal and load balanced mapping of parallel priority queues in hypercubes

We efficiently map a priority queue on the hypercube architecture in a load balanced manner, with no additional communication overhead, and present optimal parallel algorithms for performing insert and deletemin operations. Two implementations for such operations are proposed on the single port hypercube model. In a b-bandwidth, n-item priority queue in which every node contains b items in sorted order, the first implementation achieves optimal speed up of O(min{log n, b log n/log b+log log n}) for inserting b presorted items or deleting b smallest items, where b=O(n1c/) with c>1. In particular, single insertion and deletion operations are cost optimal and require O(log n/p+log p) time using O(log n/log log n) processors. The second implementation is more scalable since it uses a larger number of processors, and attains a "nearly" optimal speedup on the single hypercube. Namely, the insertion of log n presorted items or the deletion of the log n smallest items is accomplished in O(log log n2) time using O(log2 n/log log n) processors. Finally, on the slightly more powerful pipelined hypercube model, the second implementation performs log n operations in O(log log n) time using O(log2 n/log log n) processors, thus achieving an optimal speed up. To the best of our knowledge, our algorithms are the first implementations of b-bandwidth distributed priority queues, which are load balanced and yet guarantee optimal speed ups.