Rank-Sensitive Priority Queues

We introduce the rank-sensitive priority queue — a data structure that always knows the minimum element it contains, for which insertion and deletion take O(log(n/r)) time, with n being the number of elements in the structure, and r being the rank of the element being inserted or deleted (r = 1 for the minimum, r = n for the maximum). We show how several elegant implementations of rank-sensitive priority queues can be obtained by applying novel modifications to treaps and amortized balanced binary search trees, and we show that in the comparison model, the bounds above are essentially the best possible. Finally, we conclude with a case study on the use of rank-sensitive priority queues for shortest path computation.