Abstract

Priority queues are some of the most fundamental data structures. They are used directly for, say, task scheduling in operating systems. Moreover, they are essential to greedy algorithms. We study the complexity of priority queue operations on a RAM with arbitrary word size. We present exponential improvements over previous bounds, and we show tight relations to sorting. Our first result is a RAM priority queue supporting insert and extract-min operations in worst case time O(log log n) where n is the current number of keys in the queue. This is an exponential improvement over the O( p log n) bound of Fredman and Willard from STOC'90. Our algorithm is simple, and it only uses AC 0 operations, meaning that there is no hidden time dependency on the word size. Plugging this priority queue into Dijkstra's algorithm gives an O(m log log m) algorithm for the single source shortest path problem on a graph with m edges, as compared with the previous O(m p log m) bound based on Fredman...

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