Retroactive Monotonic Priority Queues via Range Searching

TL;DR

This paper introduces a fully retroactive monotonic priority queue that matches the efficiency of standard priority queues, solving an open problem by leveraging range searching techniques.

Contribution

It demonstrates that a fully retroactive monotonic priority queue can achieve optimal bounds similar to non-retroactive queues, using novel range searching methods.

Findings

Achieves $O(\log m)$ time per operation and $O(m)$ space for retroactive monotonic priority queues.

Shows that finding the minimum is a special case of range searching.

Provides a new approach to fully retroactive data structures.

Abstract

The best-known fully retroactive priority queue costs $O(\log^2 m \log \log m)$ time per operation and uses $O(m \log m)$ space, where $m$ is the number of operations performed on the data structure. In contrast, standard (non-retroactive) priority queues can cost $O(\log m)$ time per operation and use $O(m)$ space. So far, it remains open whether these bounds can be achieved for fully retroactive priority queues. In this work, we study a restricted variant of priority queues known as monotonic priority queues. First, we show that finding the minimum in a retroactive monotonic priority queue is a special case of the range-searching problem. Then, we design a fully retroactive monotonic priority queue that costs $O(\log m)$ time per operation and uses $O(m)$ space, achieving the same bounds as a standard priority queue.