Papers by Konstantinos Tsakalidis
We present optimal deterministic algorithms for constructing shallow cuttings in an arrangement o... more We present optimal deterministic algorithms for constructing shallow cuttings in an arrangement of lines in two dimensions or planes in three dimensions. Our results improve the deterministic polynomial-time algorithm of Matoušek (1992) and the optimal but randomized algorithm of Ramos (1999). This leads to efficient derandomization of previous algorithms for numerous well studied problems in computational geometry, including halfspace range reporting in 2-d and 3-d,
k nearest neighbors search in 2-d, ( k)-levels in 3-d, order-k Voronoi diagrams in 2-d, linear programming with k violations in 2-d, dynamic convex hulls in 3-d, dynamic nearest neighbor
search in 2-d, convex layers (onion peeling) in 3-d, "-nets for halfspace ranges in 3-d, and more. As a side product we also describe an optimal deterministic algorithm for constructing standard (non-shallow) cuttings in two dimensions, which is arguably simpler than the known optimal algorithms by Matoušek (1991) and Chazelle (1993).
We present I/O-efficient fully persistent B-Trees that support range searches at any version in O... more We present I/O-efficient fully persistent B-Trees that support range searches at any version in O(logBn + t/B) I/Os and updates at any version in O(logBn + log2B) amortized I/Os, using space O(m/B) disk blocks. By n we denote the number of elements in the accessed version, by m the total number of updates, by t the size of the query's output, and by B the disk block size. The result improves the previous fully persistent B-Trees of Lanka and Mays by a factor of O(logBm) for the range query complexity and O(logBn) for the update complexity. To achieve the result, we first present a new B-Tree implementation that supports searches and updates in O(logBn) I/Os, using O(n/B) blocks of space. Moreover, every update makes in the worst case a constant number of modifications to the data structure. We make these B-Trees fully persistent using an I/O-efficient method for full persistence that is inspired by the node-splitting method of Driscoll et al. The method we present is interesting...
We present the first fully dynamic worst case I/O-efficient data structures that support planar o... more We present the first fully dynamic worst case I/O-efficient data structures that support planar orthogonal \textit{3-sided range skyline reporting queries} in $\bigO (\log_{2B^\epsilon} n + \frac{t}{B^{1-\epsilon}})$ I/Os and updates in $\bigO (\log_{2B^\epsilon} n)$ I/Os, using $\bigO (\frac{n}{B^{1-\epsilon}})$ blocks of space, for $n$ input planar points, $t$ reported points, and parameter $0 \leq \epsilon \leq 1$. We obtain the result by extending Sundar's priority queues with attrition to support the operations \textsc{DeleteMin} and \textsc{CatenateAndAttrite} in $\bigO (1)$ worst case I/Os, and in $\bigO(1/B)$ amortized I/Os given that a constant number of blocks is already loaded in main memory. Finally, we show that any pointer-based static data structure that supports \textit{dominated maxima reporting queries}, namely the difficult special case of 4-sided skyline queries, in $\bigO(\log^{\bigO(1)}n +t)$ worst case time must occupy $\Omega(n \frac{\log n}{\log \log n})...
Proceedings of the 13th International Conference on Database Theory - ICDT '10, 2010
Abstract This work studies the problem of 2-dimensional searching for the 3-sided range query of ... more Abstract This work studies the problem of 2-dimensional searching for the 3-sided range query of the form [a, b] x (-∞, c] in both main and external memory, by considering a variety of input distributions. A dynamic linear main memory solution is proposed, which answers ...
Lecture Notes in Computer Science, 2014
We study the problem of rectangle enclosure: given a set of n axis-aligned rectangles on the plan... more We study the problem of rectangle enclosure: given a set of n axis-aligned rectangles on the plane, report all k pairs (r 1 , r 2 ) of input rectangles where r 1 completely encloses r 2 . This is a classic problem in the field of computational geometry [18] with applications to VLSI design, image processing, computer graphics and databases .
Lecture Notes in Computer Science, 2007
We present a set of time-efficient approaches to index objects moving on the plane to efficiently... more We present a set of time-efficient approaches to index objects moving on the plane to efficiently answer range queries about their future positions. Our algorithms are based on previously described solutions as well as on the employment of efficient data structures. Finally, an experimental evaluation is included that shows the performance, scalability and efficiency of our methods.
Optimal Deterministic Shallow Cuttings for 3D Dominance Ranges
Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, 2013
Proceedings of the 32nd symposium on Principles of database systems - PODS '13, 2013
In the planar range skyline reporting problem, the goal is to store a set P of n 2D points in a s... more In the planar range skyline reporting problem, the goal is to store a set P of n 2D points in a structure such that, given a query rectangle Q = [α1, α2] × [β1, β2], the maxima (a.k.a. skyline) of P ∩ Q can be reported efficiently. The query is 3-sided if an edge of Q is grounded, giving rise to two variants: top-open (β2 = ∞) and left-open (α1 = −∞) (symmetrically bottom-open and right-open) queries.
Lecture Notes in Computer Science, 2012
We present an efficient algorithm for the pointer machine model that preprocesses a set of n thre... more We present an efficient algorithm for the pointer machine model that preprocesses a set of n three-dimensional points in O(n log n) worst case time to construct an O(n) space data structure that supports three-dimensional dominance reporting queries in O(log n+t) worst case time, when t points are reported. Previous results achieved either O(n 2 ) worst case or O(n log n) expected preprocessing time. The novelty of our approach is that we employ persistent data structures and exploit geometric observations of previous works, in order to achieve a drastic reduction in the worst case preprocessing time.
Lecture Notes in Computer Science, 2011
We consider the dynamic two-dimensional maxima query problem. Let P be a set of n points in the p... more We consider the dynamic two-dimensional maxima query problem. Let P be a set of n points in the plane. A point is maximal if it is not dominated by any other point in P . We describe two data structures that support the reporting of the t maximal points that dominate a given query point, and allow for insertions and deletions of points in P .
Lecture Notes in Computer Science, 2013
We design compressed persistent indices that store a bit vector of size n and support a sequence ... more We design compressed persistent indices that store a bit vector of size n and support a sequence of k bit-flip update operations, such that rank and select queries at any version can be supported efficiently. In particular, we present partially and fully persistent compressed indices for offline and online updates that support all operations in time polylogarithmic in n and k. This improves upon the space or time complexities of straightforward approaches, when k = O( n log n ), which is common in biological applications. We also prove that any partially persistent index that occupies O((n + k) log(nk)) bits requires ω(1) time to support the rank query at a given version.
Theoretical Computer Science, 2014
The Priority Search Tree is the classic solution for the problem of dynamic 2-dimensional searchi... more The Priority Search Tree is the classic solution for the problem of dynamic 2-dimensional searching for the orthogonal query range of the form [a, b] × (−∞, c] (3-sided rectangle).
Data & Knowledge Engineering, 2008
We present a set of time-efficient approaches to index objects moving on the plane to efficiently... more We present a set of time-efficient approaches to index objects moving on the plane to efficiently answer range queries about their future positions. Our algorithms are based on previously described solutions as well as on the employment of efficient access methods. Finally, an experimental evaluation is included that shows the performance, scalability and efficiency of our methods.
SMaRT: A novel framework for addressing range queries over nonlinear trajectories
Journal of Systems and Software, 2015
ABSTRACT A spatiotemporal database is a database that manages both space and time information. Co... more ABSTRACT A spatiotemporal database is a database that manages both space and time information. Common examples include tracking of moving objects, intelligent transportation systems, cellular communications and meteorology monitoring. A spatiotemporal query determines the objects included in a region at a specified period of time between two date-time instants referred as time window. In the context of this work, we present SMaRT: A novel Spatiotemporal Mysql ReTrieval framework, based on MySQL and PostgreSQL database management system. Moreover, we propose a demo user interface that implements all of its capabilities, in order to help user determine the most efficient spatiotemporal query method on user-defined 2D trajectories. To our knowledge, we are the first to study and compare methods of addressing range queries on nonlinear moving object trajectories, that are represented both in dual and native dimensional space. In particular, it is the first time a theoretically efficient dual approach was implemented for nonlinear trajectories and incorporated into a well-known open-source RDBMS. An experimental evaluation is included that shows the performance and efficiency of our approach.
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Papers by Konstantinos Tsakalidis
k nearest neighbors search in 2-d, ( k)-levels in 3-d, order-k Voronoi diagrams in 2-d, linear programming with k violations in 2-d, dynamic convex hulls in 3-d, dynamic nearest neighbor
search in 2-d, convex layers (onion peeling) in 3-d, "-nets for halfspace ranges in 3-d, and more. As a side product we also describe an optimal deterministic algorithm for constructing standard (non-shallow) cuttings in two dimensions, which is arguably simpler than the known optimal algorithms by Matoušek (1991) and Chazelle (1993).
k nearest neighbors search in 2-d, ( k)-levels in 3-d, order-k Voronoi diagrams in 2-d, linear programming with k violations in 2-d, dynamic convex hulls in 3-d, dynamic nearest neighbor
search in 2-d, convex layers (onion peeling) in 3-d, "-nets for halfspace ranges in 3-d, and more. As a side product we also describe an optimal deterministic algorithm for constructing standard (non-shallow) cuttings in two dimensions, which is arguably simpler than the known optimal algorithms by Matoušek (1991) and Chazelle (1993).