Strictly Implicit Priority Queues: On the Number of Moves and Worst-Case Time

The binary heap of Williams (1964) is a simple priority queue characterized by only storing an array containing the elements and the number of elements n – here denoted a strictly implicit priority queue. We introduce two new strictly implicit priority queues. The first structure supports amortized O(1) time Insert and O(logn) time ExtractMin operations, where both operations require amortized O(1) element moves. No previous implicit heap with O(1) time Insert supports both operations with O(1) moves. The second structure supports worst-case O(1) time Insert and O(logn) time (and moves) ExtractMin operations. Previous results were either amortized or needed O(logn) bits of additional state information between operations.