Computer Science > Computational Geometry
[Submitted on 7 Jul 2021 (v1), last revised 24 Feb 2023 (this version, v2)]
Title:Oblivious Median Slope Selection
View PDFAbstract:We study the median slope selection problem in the oblivious RAM model. In this model memory accesses have to be independent of the data processed, i.e., an adversary cannot use observed access patterns to derive additional information about the input. We show how to modify the randomized algorithm of Matoušek (1991) to obtain an oblivious version with $\mathcal{O}(n \log^2 n)$ expected time for $n$ points in $\mathbb{R}^2$. This complexity matches a theoretical upper bound that can be obtained through general oblivious transformation. In addition, results from a proof-of-concept implementation show that our algorithm is also practically efficient.
Submission history
From: Thore Thießen [view email][v1] Wed, 7 Jul 2021 13:10:13 UTC (58 KB)
[v2] Fri, 24 Feb 2023 11:29:57 UTC (57 KB)
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