23 research outputs found
I/O-Efficient Dynamic Planar Range Skyline Queries
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 input planar points,
reported points, and parameter . 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 space, by adapting a similar lower bounding argument for
planar 4-sided range reporting queries.Comment: Submitted to SODA 201
CONTINUOUS MULTIQUERIES K-DOMINANT SKYLINE ON ROAD NETWORK
The increasing use of mobile devices makes spatial data worthy of consideration. To get maximum results, users often look for the best from a collection of objects. Among the algorithms that can be used is the skyline query. The algorithm looks for all objects that are not dominated by other objects in all of its attributes. However, data that has many attributes makes the query output a lot of objects so it is less useful for the user. k-dominant skyline queries can be a solution to reduce the output. Among the challenges is the use of skyline queries with spatial data and the many user preferences in finding the best object. This study proposes IKSR: the k-dominant skyline query algorithm that works in a road network environment and can process many queries that have the same subspace in one processing. This algorithm combines queries that operate on the same subspace and set of objects with different k values by computing from the smallest to the largest k. Optimization occurs when some data for larger k are precomputed when calculating the result for the smallest k so the Voronoi cell computing is not repeated. Testing is done by comparing with the naïve algorithm without precomputation. IKSR algorithm can speed up computing time two to three times compared to naïve algorithm
Probabilistic Skyline Queries over Uncertain Moving Objects
Data uncertainty inherently exists in a large number of applications due to factors such as limitations of measuring equipments, update delay, and network bandwidth. Recently, modeling and querying uncertain data have attracted considerable attention from the database community. However, how to perform advanced analysis on uncertain data remains an interesting question. In this paper, we focus on the execution of skyline computation over uncertain moving objects. We propose a novel probabilistic skyline model where an uncertain object may take a probability to be in the skyline at a certain time point, therefore a p-t-skyline contains those moving objects whose skyline probabilities are at least p at time point t. Computing probabilistic skyline over a large number of uncertain moving objects is a daunting task in practice. In order to efficiently compute the probabilistic skyline query, we propose a discrete-and-conquer strategy, which follows the sampling-bounding-pruning-refining procedure. To further reduce the skyline computation cost, we propose an enhanced framework that is based on a multi-dimensional indexing structure combined with the discrete-and-conquer strategy. Through extensive experiments with synthetic datasets, we show that the framework can efficiently support skyline queries over uncertain moving object and is scalable on large data sets
I/O-Efficient Planar Range Skyline and Attrition Priority Queues
In the planar range skyline reporting problem, we store a set P of n 2D
points in a structure such that, given a query rectangle Q = [a_1, a_2] x [b_1,
b_2], the maxima (a.k.a. skyline) of P \cap Q can be reported efficiently. The
query is 3-sided if an edge of Q is grounded, giving rise to two variants:
top-open (b_2 = \infty) and left-open (a_1 = -\infty) queries.
All our results are in external memory under the O(n/B) space budget, for
both the static and dynamic settings:
* For static P, we give structures that answer top-open queries in O(log_B n
+ k/B), O(loglog_B U + k/B), and O(1 + k/B) I/Os when the universe is R^2, a U
x U grid, and a rank space grid [O(n)]^2, respectively (where k is the number
of reported points). The query complexity is optimal in all cases.
* We show that the left-open case is harder, such that any linear-size
structure must incur \Omega((n/B)^e + k/B) I/Os for a query. We show that this
case is as difficult as the general 4-sided queries, for which we give a static
structure with the optimal query cost O((n/B)^e + k/B).
* We give a dynamic structure that supports top-open queries in O(log_2B^e
(n/B) + k/B^1-e) I/Os, and updates in O(log_2B^e (n/B)) I/Os, for any e
satisfying 0 \le e \le 1. This leads to a dynamic structure for 4-sided queries
with optimal query cost O((n/B)^e + k/B), and amortized update cost O(log
(n/B)).
As a contribution of independent interest, we propose an I/O-efficient
version of the fundamental structure priority queue with attrition (PQA). Our
PQA supports FindMin, DeleteMin, and InsertAndAttrite all in O(1) worst case
I/Os, and O(1/B) amortized I/Os per operation.
We also add the new CatenateAndAttrite operation that catenates two PQAs in
O(1) worst case and O(1/B) amortized I/Os. This operation is a non-trivial
extension to the classic PQA of Sundar, even in internal memory.Comment: Appeared at PODS 2013, New York, 19 pages, 10 figures. arXiv admin
note: text overlap with arXiv:1208.4511, arXiv:1207.234