Comparator networks for binary heap construction

Comparator networks for constructing binary heaps of size n are presented which have size O(nloglogn) and depth O(logn). A lower bound of nloglogn-O(n) for the size of any heap construction network is also proven, implying that the networks presented are within a constant factor of optimal. We give a tight relation between the leading constants in the size of selection networks and in the size of heap construction networks.