The relaxed min-max heap

A data structure that implements a mergeable double-ended priority queue, namely therelaxed min-max heap, is presented. A relaxed min-max heap ofn items can be constructed inO(n) time. In the worst case, operationsfind_min() andfind_max() can be performed in constant time, while each of the operationsmerge(),insert(),delete_min(),delete_max(),decrease_key(), anddelete_key() can be performed inO(logn) time. Moreover,insert() hasO(1) amortized running time. If lazy merging is used,merge() will also haveO(1) worst-case and amortized time. The relaxed min-max heap is the first data structure that achieves these bounds using only two pointers (puls one bit) per item.