A parallel heap of node capacity r keeps all the r items at each of its individual nodes sorted. The parallel heap sorts the new items to be inserted before starting its insert-update process. These new items start at the root node, and ‘ sink ’ toward their target node at the bottom of the parallel heap after being repeatedly merged with the items at the intervening nodes, and by carrying down the larger items each time. Likewise, after a deletion of some Ic 5 r items, k items are brought in at the root as substitute items from the bottom of the parallel heap, and merged with the remaining (r - Ic) items of the root. Since the parallel heap property would be destroyed at the root because of this, a delete-update process begins at the root. This involves merging the items at the root, and its two children, keeping the smallest r at the root, placing the next smallest T items at the left child if its largest item was bigger than that of the right child, else placing them at the right child. Finally, the largest r items are placed at the other child, and a delete-update process is initiated at that child. This process repeats until the parallel heap property gets satisfied. These insert- and delete-update processes are carried out in a pipeline fashion for overall optimal.