The content discusses the problem of sorting in the evolving data model, where the true underlying total order of the data changes gradually over time. The goal is to maintain an ordering that remains close to the true order.
The key contributions are:
Analysis of a simple randomized algorithm called Naïve Sort, which samples a random pair of adjacent items in each step and swaps them if they are out of order.
Showing that Naïve Sort achieves optimal total deviation of O(n) and optimal maximum deviation of O(log n), under a generalized model with:
The analysis uses a novel potential function argument that inserts "gaps" in the list of items, and a general framework that separates the analysis of sorting from the evolution steps.
The results settle conjectures from prior work, and provide theoretical support for the empirical evidence that simple quadratic algorithms are optimal and robust for sorting evolving data.
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by Marcos Kiwi,... klokken arxiv.org 04-15-2024
https://arxiv.org/pdf/2404.08162.pdfDypere Spørsmål