Parallel heap operations on EREW PRAM: summary of results

The authors present parallel algorithms for heap operations on an EREW PRAM. They first present a parallel heap construction algorithm with p processors running in O(n/p+logp) time. It takes 3.625n/p+4log p time in the worst case. The algorithm is optimal when p=θ(n/logn). They then propose a method to delete the root of a heap in parallel. To facilitate dynamic processor allocation, a data structure is developed in a preparatory step using O((n/logn)^1-1/p) processors in O(logp) time. A sequence of root deletion operations is realized such that each of these operations takes O((logn)/p+logp+loglogn) time using p processors. The authors also suggest an O((logn)/p+log p) time optimal parallel insert algorithm using p processors. When p=θ((logn)/loglogn), both algorithms run in O(loglogn) time. The algorithms can also be extended to a parallel algorithm for deleting an element from a heap, given the address of the element