Cloning Voronoi diagrams via retroactive data structures
Matthew Dickerson,David Eppstein,Michael T. Goodrich +2 more
- pp 362-373
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TLDR
This work addresses the problem of replicating a Voronoi diagram V(S) of a planar point set S by making proximity queries and provides one of the first natural algorithmic applications of retroactive data structures.Abstract:
We address the problem of replicating a Voronoi diagram V(S) of a planar point set S by making proximity queries: 1. the exact location of the nearest site(s) in S 2. the distance to and label(s) of the nearest site(s) in S 3. a unique label for every nearest site in S.
In addition to showing the limits of nearest-neighbor database security, our methods also provide one of the first natural algorithmic applications of retroactive data structures.read more
Citations
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Proceedings ArticleDOI
Exploring Privacy Preservation in Outsourced K-Nearest Neighbors with Multiple Data Owners
TL;DR: This work presents the first framing and exploration of privacy preservation in an outsourced k-NN system with multiple data owners, and proposes a privacy-preserving alternative system supporting kernel density estimation using a Gaussian kernel, a classification algorithm from the same family as k-nn.
Book ChapterDOI
Fully retroactive approximate range and nearest neighbor searching
TL;DR: In this paper, the authors describe fully retroactive dynamic data structures for approximate range reporting and approximate nearest neighbor reporting, and show how to maintain, for any positive constant d, a set of n points in ℝd indexed by time such that we can perform insertions or deletions at any point in the timeline in O(logn) amortized time.
Posted Content
Upper and Lower Bounds for Fully Retroactive Graph Problems.
Monika Henzinger,Xiaowei Wu +1 more
TL;DR: It is shown that under the OMv conjecture (proposed by Henzinger et al. (STOC 2015)), there does not exist fully retroactive data structures maintaining connectivity or MSF, or incremental fully Retroactive data structure maintaining the maximum degree with $O(n^{1-\epsilon})$ time per operation, for any constant $\epsilons > 0$.
Journal ArticleDOI
Fully Retroactive Priority Queues using Persistent Binary Search Trees
TL;DR: This work presents how to implement a data structure to a fully retroactive version of a priority queue through persistent self-balanced binary search trees in polylogarithmic time and shows that the average performance of the proposed algorithm is better in terms of processing times than the other algorithms, despite the high constants in its complexity.
Book ChapterDOI
Upper and Lower Bounds for Fully Retroactive Graph Problems
Monika Henzinger,Xiaowei Wu +1 more
TL;DR: In this article, a fully retroactive data structure (FRS) was proposed to handle operations that change the sequence S of updates, which can handle queries at any time t: a query at time t is answered using only the updates of S up to time t.
References
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