Cloning Voronoi Diagrams via Retroactive Data Structures

Dickerson, Matthew; Eppstein, David; Goodrich, Michael T.

doi:10.1007/978-3-642-15775-2_31

Cited by 6 publications

(5 citation statements)

References 44 publications

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“…The notion of retroactive data structure helps to solve problems, such as dynamic shortest path problem (Sunita and Garg, 2018) and geometric problems, such as cloning Voronoi diagrams (Dickerson et al, 2010) and nearest neighbor search (Goodrich and Simons, 2011 time per operation. The data structure also supports the operation of determining the time at which an element was deleted from the data structure in O(lg 2 m).…”

Section: Related Workmentioning

confidence: 99%

Fully Retroactive Priority Queues using Persistent Binary Search Trees

Andrade¹,

Seabra²

2020

Journal of Computer Science

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Classic dynamic data structures maintains itself subject to sequence S of operations and answer queries using the latest version of the data structure. Retroactive data structures are those which allow making a modification or a query in any version of this data structure through its timeline. These data structures are used in some geometric problems and in problems related with graphs, such as the minimum path problem in dynamic graphs. 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. We use these data structures to improve the performance merging two versions of partially retroactive priority queues. The empirical analysis showed 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.

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Section: Related Workmentioning

confidence: 99%

Fully Retroactive Priority Queues using Persistent Binary Search Trees

Andrade¹,

Seabra²

2020

Journal of Computer Science

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“…We note that prior work [7] has developed algorithms for cloning the Voronoi diagram of 1-NN using only queries if the query responses contain the exact location of the nearest neighbor or the distance and label of the nearest neighbor. If only the nearest neighbor label is returned, then the algorithm provides an approximate cloning.…”

Section: Distance-learning Attacks In the Do-q Modelmentioning

confidence: 99%

“…Also we focus on a system model where query responses do not contain the distance (which we considered an already broken construction). The algorithms in [7] require at least distance in the query response to conduct exact cloning.…”

Section: Distance-learning Attacks In the Do-q Modelmentioning

confidence: 99%

Exploring Privacy Preservation in Outsourced K-Nearest Neighbors with Multiple Data Owners

Shin

Paxson

2015

Proceedings of the 2015 ACM Workshop on Cloud Computing Security Workshop

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The k-nearest neighbors (k-NN) algorithm is a popular and effective classification algorithm. Due to its large storage and computational requirements, it is suitable for cloud outsourcing. However, k-NN is often run on sensitive data such as medical records, user images, or personal information. It is important to protect the privacy of data in an outsourced k-NN system.Prior works have all assumed the data owners (who submit data to the outsourced k-NN system) are a single trusted party. However, we observe that in many practical scenarios, there may be multiple mutually distrusting data owners. In this work, we present the first framing and exploration of privacy preservation in an outsourced k-NN system with multiple data owners. We consider the various threat models introduced by this modification. We discover that under a particularly practical threat model that covers numerous scenarios, there exists a set of adaptive attacks that breach the data privacy of any exact k-NN system. The vulnerability is a result of the mathematical properties of k-NN and its output. Thus, we propose a privacy-preserving alternative system supporting kernel density estimation using a Gaussian kernel, a classification algorithm from the same family as k-NN. In many applications, this similar algorithm serves as a good substitute for k-NN. We additionally investigate solutions for other threat models, often through extensions on prior single data owner systems.

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“…For this 1-dimensional retroactive data structuring problem, Blelloch and Giora and Kaplan give data structures that support queries and updates in O(log n) time. Dickerson et al [22] describe a retroactive data structure for maintaining the lower envelope of a set of parabolic arcs and give an application of this structure to the problem of cloning a Voronoi diagram from a server that answers nearest-neighbor queries.…”

Section: Related Workmentioning

confidence: 99%

Fully Retroactive Approximate Range and Nearest Neighbor Searching

Goodrich

Simons

2011

Algorithms and Computation

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We describe fully retroactive dynamic data structures for approximate range reporting and approximate nearest neighbor reporting. We show how to maintain, for any positive constant d, a set of n points in R d indexed by time such that we can perform insertions or deletions at any point in the timeline in O(log n) amortized time. We support, for any small constant > 0, (1 + )-approximate range reporting queries at any point in the timeline in O(log n + k) time, where k is the output size. We also show how to answer (1 + )-approximate nearest neighbor queries for any point in the past or present in O(log n) time. arXiv:1109.0312v1 [cs.CG] 1 Sep 2011 2. Represent each d-dimensional point as a line segment in d + 1 dimensions.

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Cloning Voronoi Diagrams via Retroactive Data Structures

Cited by 6 publications

References 44 publications

Fully Retroactive Priority Queues using Persistent Binary Search Trees

Fully Retroactive Priority Queues using Persistent Binary Search Trees

Exploring Privacy Preservation in Outsourced K-Nearest Neighbors with Multiple Data Owners

Fully Retroactive Approximate Range and Nearest Neighbor Searching

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