A Framework for Speeding Up Priority-Queue Operations

We introduce a framework for reducing the number of element comparisons performed in priority-queue operations. In particular, we give a priority queue which guarantees the worst-case cost of O(1) per minimum finding and insertion, and the worst-case cost of O(log n) with at most log n+O(1) element comparisons per minimum deletion and deletion, improving the bound of 2 logn+ O(1) on the number of element comparisons known for binomial queues. Here, n denotes the number of elements stored in the data structure prior to the operation in question, and log n equals max {1, log 2 n}. We also give a priority queue that provides, in addition to the above-mentioned methods, the priority-decrease (or decrease-key) method. This priority queue achieves the worst-case cost of O(1) per minimum finding, insertion, and priority decrease; and the worst-case cost of O(log n) with at most log n+O(log log n) element comparisons per minimum deletion and deletion. CR Classification. E.1 [Data Structures]: Lists, stacks, and queues; E.2 [Data Storage Representations]: Linked representations; F.2.2 [Analysis of Algorithms and Problem Complexity]: sorting and searching