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230
The Skyline Operator
 IN ICDE
, 2001
"... We propose to extend database systems by a Skyline operation. This operation filters out a set of interesting points from a potentially large set of data points. A point is interesting if it is not dominated by any other point. For example, a hotel might be interesting for somebody traveling to Nass ..."
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Cited by 567 (3 self)
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We propose to extend database systems by a Skyline operation. This operation filters out a set of interesting points from a potentially large set of data points. A point is interesting if it is not dominated by any other point. For example, a hotel might be interesting for somebody traveling to Nassau if no other hotel is both cheaper and closer to the beach. We show how SQL can be extended to pose Skyline queries, present and evaluate alternative algorithms to implement the Skyline operation, and show how this operation can be combined with other database operations (e.g., join and Top N).
Shooting Stars in the Sky: An Online Algorithm for Skyline Queries
 In VLDB
, 2002
"... Skyline queries ask for a set of interesting points from a potentially large set of data points. If we are traveling, for instance, a restaurant might be interesting if there is no other restaurant which is nearer, cheaper, and has better food. Skyline queries retrieve all such interesting restauran ..."
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Cited by 284 (0 self)
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Skyline queries ask for a set of interesting points from a potentially large set of data points. If we are traveling, for instance, a restaurant might be interesting if there is no other restaurant which is nearer, cheaper, and has better food. Skyline queries retrieve all such interesting restaurants so that the user can choose the most promising one. In this paper, we present a new online algorithm that computes the Skyline. Unlike most existing algorithms that compute the Skyline in a batch, this algorithm returns the first results immediately, produces more and more results continuously, and allows the user to give preferences during the running time of the algorithm so that the user can control what kind of results are produced next (e.g., rather cheap or rather near restaurants).
An optimal and progressive algorithm for skyline queries
 In SIGMOD
, 2003
"... The skyline of a set of ddimensional points contains the points that are not dominated by any other point on all dimensions. Skyline computation has recently received considerable attention in the database community, especially for progressive (or online) algorithms that can quickly return the firs ..."
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Cited by 225 (16 self)
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The skyline of a set of ddimensional points contains the points that are not dominated by any other point on all dimensions. Skyline computation has recently received considerable attention in the database community, especially for progressive (or online) algorithms that can quickly return the first skyline points without having to read the entire data file. Currently, the most efficient algorithm is NN (nearest neighbors), which applies the divideandconquer framework on datasets indexed by Rtrees. Although NN has some desirable features (such as high speed for returning the initial skyline points, applicability to arbitrary data distributions and dimensions), it also presents several inherent disadvantages (need for duplicate elimination if d>2, multiple accesses of the same node, large space overhead). In this paper we develop BBS (branchandbound skyline), a progressive algorithm also based on nearest neighbor search, which is IO optimal, i.e., it performs a single access only to those Rtree nodes that may contain skyline points. Furthermore, it does not retrieve duplicates and its space overhead is significantly smaller than that of NN. Finally, BBS is simple to implement and can be efficiently applied to a variety of alternative skyline queries. An analytical and experimental comparison shows that BBS outperforms NN (usually by orders of magnitude) under all problem instances. 1.
Progressive Skyline Computation in Database Systems
 ACM TRANS. DATABASE SYST
, 2005
"... The skyline of a ddimensional dataset contains the points that are not dominated by any other point on all dimensions. Skyline computation has recently received considerable attention in the database community, especially for progressive methods that can quickly return the initial results without r ..."
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Cited by 205 (13 self)
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The skyline of a ddimensional dataset contains the points that are not dominated by any other point on all dimensions. Skyline computation has recently received considerable attention in the database community, especially for progressive methods that can quickly return the initial results without reading the entire database. All the existing algorithms, however, have some serious shortcomings which limit their applicability in practice. In this article we develop branch skyline (BBS), an algorithm based on nearestneighbor search, which is I/O optimal, that is, it performs a single access only to those nodes that may contain skyline points. BBS is simple to implement and supports all types of progressive processing (e.g., user preferences, arbitrary dimensionality, etc). Furthermore, we propose several interesting variations of skyline computation, and show how BBS can be applied for their efficient processing.
Efficient distributed skylining for web information systems
 IN EDBT
, 2004
"... Though skyline queries already have claimed their place in retrieval over central databases, their application in Web information systems up to now was impossible due to the distributed aspect of retrieval over Web sources. But due to the amount, variety and volatile nature of information accessible ..."
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Cited by 123 (14 self)
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Though skyline queries already have claimed their place in retrieval over central databases, their application in Web information systems up to now was impossible due to the distributed aspect of retrieval over Web sources. But due to the amount, variety and volatile nature of information accessible over the Internet extended query capabilities are crucial. We show how to efficiently perform distributed skyline queries and thus essentially extend the expressiveness of querying today’s Web information systems. Together with our innovative retrieval algorithm we also present useful heuristics to further speed up the retrieval in most practical cases paving the road towards meeting even the realtime challenges of online information services. We discuss performance evaluations and point to open problems in the concept and application of skylining in modern information systems. For the curse of dimensionality, an intrinsic problem in skyline queries, we propose a novel sampling scheme that allows to get an early impression of the skyline for subsequent query refinement.
On the average number of maxima in a set of vectors and applications
 Journal of the ACM
, 1978
"... ABSTRACT. A maximal vector of a set ~s one which is not less than any other vector m all components We derive a recurrence relation for computing the average number of maxunal vectors m a set of n vectors m dspace under the assumpUon that all (nl) a relative ordermgs are equally probable. Solving t ..."
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Cited by 105 (1 self)
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ABSTRACT. A maximal vector of a set ~s one which is not less than any other vector m all components We derive a recurrence relation for computing the average number of maxunal vectors m a set of n vectors m dspace under the assumpUon that all (nl) a relative ordermgs are equally probable. Solving the recurrence shows that the average number of maxmaa is O((ln n) a~) for fixed d We use this result to construct an algorithm for finding all the maxima that have expected running tmae hnear m n (for sets of vectors drawn under our assumptions) We then use the result to find an upper bound on the expected number of convex hull points m a random point set KE ~ WORDS AND eHRASES maxtma of a set of vectors, average number of maxtma, expectedtsme algorithms, analysts of algorithms, convex hulls, dynamtc programming CR CATEGORIES " 5 25, 5.39, 5.42 1.
Probabilistic skylines on uncertain data
 In Proceedings of the 33rd International Conference on Very Large Data Bases (VLDB’07), Viena
, 2007
"... Uncertain data are inherent in some important applications. Although a considerable amount of research has been dedicated to modeling uncertain data and answering some types of queries on uncertain data, how to conduct advanced analysis on uncertain data remains an open problem at large. In this pap ..."
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Cited by 103 (19 self)
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Uncertain data are inherent in some important applications. Although a considerable amount of research has been dedicated to modeling uncertain data and answering some types of queries on uncertain data, how to conduct advanced analysis on uncertain data remains an open problem at large. In this paper, we tackle the problem of skyline analysis on uncertain data. We propose a novel probabilistic skyline model where an uncertain object may take a probability to be in the skyline, and a pskyline contains all the objects whose skyline probabilities are at least p. Computing probabilistic skylines on large uncertain data sets is challenging. We develop two efficient algorithms. The bottomup algorithm computes the skyline probabilities of some selected instances of uncertain objects, and uses those instances to prune other instances and uncertain objects effectively. The topdown algorithm recursively partitions the instances of uncertain objects into subsets, and prunes subsets and objects aggressively. Our experimental results on both the real NBA player data set and the benchmark synthetic data sets show that probabilistic skylines are interesting and useful, and our two algorithms are efficient on large data sets, and complementary to each other in performance. 1.
Selecting Stars: The k Most Representative Skyline Operator
 In Proc. of the Int. IEEE Conf. on Data Engineering (ICDE
, 2007
"... Skyline computation has many applications including multicriteria decision making. In this paper, we study the problem of selecting k skyline points so that the number of points, which are dominated by at least one of these k skyline points, is maximized. We first present an efficient dynamic progr ..."
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Cited by 93 (3 self)
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Skyline computation has many applications including multicriteria decision making. In this paper, we study the problem of selecting k skyline points so that the number of points, which are dominated by at least one of these k skyline points, is maximized. We first present an efficient dynamic programming based exact algorithm in a 2dspace. Then, we show that the problem is NPhard when the dimensionality is 3 or more and it can be approximately solved by a polynomial time algorithm with the guaranteed approximation ratio 1 − 1 e. To speedup the computation, an efficient, scalable, indexbased randomized algorithm is developed by applying the FM probabilistic counting technique. A comprehensive performance evaluation demonstrates that our randomized technique is very efficient, highly accurate, and scalable. 1.
Maximal Vector Computation in Large Data Sets
 IN VLDB
, 2005
"... Finding the maximals in a collection of vectors is relevant to many applications. The maximal set is related to the convex hull  and hence, linear optimization  and nearest neighbors. The maximal vector problem has resurfaced with the advent of skyline queries for relational databases and skyl ..."
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Cited by 89 (1 self)
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Finding the maximals in a collection of vectors is relevant to many applications. The maximal set is related to the convex hull  and hence, linear optimization  and nearest neighbors. The maximal vector problem has resurfaced with the advent of skyline queries for relational databases and skyline algorithms that are external and relationally well behaved. The initial
Catching the best views of skyline: A semantic approach based on decisive subspaces
 In VLDB
, 2005
"... The skyline operator is important for multicriteria decision making applications. Although many recent studies developed efficient methods to compute skyline objects in a specific space, the fundamental problem on the semantics of skylines remains open: Why and in which subspaces is (or is not) an o ..."
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Cited by 87 (12 self)
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The skyline operator is important for multicriteria decision making applications. Although many recent studies developed efficient methods to compute skyline objects in a specific space, the fundamental problem on the semantics of skylines remains open: Why and in which subspaces is (or is not) an object in the skyline? Practically, users may also be interested in the skylines in any subspaces. Then, what is the relationship between the skylines in the subspaces and those in the superspaces? How can we effectively analyze the subspace skylines? Can we efficiently compute skylines in various subspaces? In this paper, we investigate the semantics of skylines, propose the subspace skyline analysis, and extend the fullspace skyline computation to subspace skyline computation. We introduce a novel notion of skyline group which essentially is a group of objects that are coincidentally in the skylines of some subspaces. We identify the decisive subspaces that qualify skyline groups in the subspace skylines. The new notions concisely capture the semantics and the structures of skylines in various subspaces. Multidimensional rollup and drilldown analysis is introduced. We also develop