On the Power of Structural Violations in Priority Queues

We give a priority queue that guarantees the worstcase cost of Θ(1) per minimum finding, insertion, and decrease; and the worst-case cost of Θ(lg n) with at most lg n + O( √ lg n) element comparisons per deletion. Here, n denotes the number of elements stored in the data structure prior to the operation in question, and lg n is a shorthand for max {1, log2 n}. In contrast to a run-relaxed heap, which allows heaporder violations, our priority queue relies on structural violations. By mimicking a priority queue that allows heap-order violations with one that only allows structural violations, we improve the bound on the number of element comparisons per deletion to lg n + O(lg lg n).