Strictly implicit priority queues: On the number of moves and worst-case time

Abstract

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(log n) time EXTRACT- MIN 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(log n) time (and moves) EXTRACTMIN operations. Previous results were either amortized or needed O(log n) bits of additional state information between operations.