ISB-Tree: A New Indexing Scheme with Efficient Expected Behaviour

Proceedings of the 13th International Conference on Database Theory

et al. 2010

This work studies the problem of 2-dimensional searching for the 3-sided range query of the form [a, b] × (−∞, c] in both main and external memory, by considering a variety of input distributions. A dynamic linear main memory solution is proposed, which answers 3-sided queries in O(log n + t) worst case time and scales with O(log log n) expected with high probability update time, under continuous µ-random distributions of the x and y coordinates, where n is the current number of stored points and t is the size of the query output. Our expected update bound constitutes a considerable improvement over the O(log n) update time bound achieved by the classic Priority Search Tree of McCreight [23], as well as over the Fusion Priority Search Tree of Willard [30], which requires O( log n log log n ) time for all operations. Moreover, we externalize this solution, gaining O(log B n + t/B) worst case and O(logBlogn) amortized expected with high probability I/Os for query and update operations respectively, where B is the disk block size. Then, combining the Modified Priority Search Tree [27] with the Priority Search Tree [23], we achieve a query time of O(log log n + t) expected with high probability and an update time of O(log log n) expected with high probability, under the assumption that the x-coordinates are continuously drawn from a smooth distribution and the ycoordinates are continuously drawn from a more restricted class of distributions. The total space is linear. Finally, we externalize this solution, obtaining a dynamic data strucPermission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. ICDT 2010, March 22-25, 2010, Lausanne, Switzerland. Copyright 2010 ture that answers 3-sided queries in O(log B log n + t/B) I/Os expected with high probability, and it can be updated in O(log B log n) I/Os amortized expected with high probability and consumes O(n/B) space, under the same assumptions.

Section: Discussionmentioning

confidence: 99%

Section: Interpolation Search Treesmentioning

confidence: 99%

Section: The Solution For the Smooth And The Restricted Distributionsmentioning

confidence: 99%

See 1 more Smart Citation

Efficient processing of 3-sided range queries with probabilistic guarantees

Kaporis

Papadopoulos

Proceedings of the 13th International Conference on Database Theory

et al. 2010

“…TS-Privacy-Aware-RQ Query transformation is used (denote that u m i n is a positive lower threshold). Moreover, our method will incorporate the Lazy B-tree [39] indexing scheme (Source code of Lazy B-tree index is free available at the following URL: http://www.ionio.gr/sioutas/ New-Software.htm), since the latter can handle update queries in optimal (constant) number of block-transfers (I/Os). Thus, we get Algorithm 7 and 8.…”

Section: Rq Querymentioning

confidence: 99%

Uncertainty for Privacy and 2-Dimensional Range Query Distortion

Journal of Computing Science and Engineering

Magkos

Karydis

et al. 2011

Self Cite

In this work, we study the problem of privacy-preservation data publishing in moving objects databases. In particular, the trajectory of a mobile user in a plane is no longer a polyline in a two-dimensional space, instead it is a two-dimensional surface of fixed width 2A defines the semi-diameter of the minimum spatial circular extent that must replace the real location of the mobile user on the XY-plane, in the anonymized (kNN) request. The desired anonymity is not achieved and the entire system becomes vulnerable to attackers, since a malicious attacker can observe that during the time, many of the neighbors' ids change, except for a small number of users. Thus, we reinforce the privacy model by clustering the mobile users according to their motion patterns in (u, θ) plane, where u and θ define the velocity measure and the motion direction (angle) respectively. In this case, the anonymized (kNN) request looks up neighbors, who belong to the same cluster with the mobile requester in (u, θ) space: Thus, we know that the trajectory of the k-anonymous mobile user is within this surface, but we do not know exactly where. We transform the surface's boundary poly-lines to dual points and we focus on the information distortion introduced by this space translation. We develop a set of efficient spatiotemporal access methods and we experimentally measure the impact of information distortion by comparing the performance results of the same spatiotemporal range queries executed on the original database and on the anonymized one. Category: Smart and intelligent computing

“…Moreover, our method will incorporate the Lazy B-tree [10] indexing scheme, since the latter can handle update queries in optimal (constant) number of block-transfers (I/Os). As a result, we get Algorithm 4.…”

Section: The Proposed Algorithm For Privacy-aware Indexingmentioning

confidence: 99%

Uncertainty for Anonymity and 2-Dimensional Range Query Distortion

Privacy in Statistical Databases

Magkos

Karydis

et al. 2010

Self Cite

Abstract. In this work, we study the problem of anonymity-preserving data publishing in moving objects databases. In particular, the trajectory of a mobile user on the plane is no longer a polyline in a two-dimensional space, instead it is a two-dimensional surface: we know that the trajectory of the mobile user is within this surface, but we do not know exactly where. We transform the surface's boundary poly-lines to dual points and we focus on the information distortion introduced by this space translation. We develop a set of efficient spatio-temporal access methods and we experimentally measure the impact of information distortion by comparing the performance results of the same spatio-temporal range queries executed on the original database and on the anonymized one.