Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Castro, Lucas, de Freitas, Rosiane
Institution: Universidade Federal do Amazonas
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G3023881574, G5532323617
OpenAlex ID: W4415272152
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