Skyline Points Research Articles

Decisive skyline queries for truly balancing multiple criteria

Skyline queries have emerged as an increasingly popular tool for identifying a set of interesting objects that balance different user-specified criteria. Although in several applications the user aims to detect data objects that have values as good as possible in all specified criteria, skyline queries fail to identify only those objects. Instead, objects whose values are good in a subset of the given criteria are also included in the skyline set, even though they may take arbitrarily bad values in the remaining criteria. To alleviate this shortcoming, we study the decisive subspaces that express the semantics of skyline points and determine skyline membership. We propose a novel alternative query, called decisive skyline query, which retrieves a set of points that balance all specified criteria. We study two variants of the proposed query, the strict variant, which retrieves only the subset of skyline points that have the full data space as decisive subspace, and the relaxed variant, which imposes the decisive semantics in a more flexible way. Furthermore, we present pruning properties that accelerate the process of finding the decisive skyline set. Capitalizing on these pruning properties, we propose a novel efficient algorithm for computing decisive skyline points. Our experimental study, which employs both synthetic and real data sets for various experimental setups, demonstrates the efficiency and effectiveness of our algorithm, and shows that the newly proposed query is more intuitive and informative for the user.

Efficiently computing Pareto optimal G-skyline query in wireless sensor network

There are much data transmitted from sensors in wireless sensor network. How to mine vital information from these large amount of data is very important for decision-making. Aiming at mining more interesting information for users, the skyline technology has attracted more attention due to its widespread use for multi-criteria decision-making. The point which is not dominated by any other points can be called skyline point. The skyline consists of all these points which are candidates for users. However, traditional skyline which consists of individual points is not suitable for combinations. To address this gap, we focus on the group skyline query and propose efficient algorithm to computing the Pareto optimal group-based skyline (G-skyline). We propose multiple query windows to compute key skyline layers, then optimize the method to compute directed skyline graph, finally introduce primary points definition and propose a fast algorithm based on it to compute G-skyline groups directly and efficiently. The experiments on the real-world sensor data set and the synthetic data set show that our algorithm performs more efficiently than the existing algorithms.

Progressive approaches to flexible group skyline queries

The G-Skyline (GSky) query is formulated to report optimal groups that are not dominated by any other group of the same size. Particularly, a given group $$G_1$$ dominates another group $$G_2$$ if for any point $$p\in G_1$$ , p dominates or equals to points $$p{'}\in G_2$$ ; at the same time, there is at least one point p dominating $$p{'}$$ . Most existing group skyline queries need to calculate an aggregate point for each group. Compared to these queries, the GSky query is more practical because it avoids specifying an aggregate function which leads to miss important results containing non-skyline points. This means the GSky query can get much more comprehensive query results which not only contain the G-Skylines consisting of skyline points but also the G-Skylines including non-skyline points. Here, a non-skyline point is dominated by another point in a given data set. However, the GSky query usually returns too many results, making it a big burden for users to pick out their expected results. To address these issues, we investigate a flexible group skyline query, namely Flexible G-Skyline (FGSky) query, which is flexible and practical for directly computing the optimal groups on the basis of user preferences. In this paper, we formulate the FGSky query, identify its properties, and present effective pruning strategies. Besides, we propose progressive algorithms for the FGSky query where a grouping strategy and a layered strategy are utilized to get better query performance. Through extensive experiments on both synthetic and real data sets, we demonstrate the efficiency, effectiveness, and progressiveness of the proposed algorithms.

Skyline computation over multiple points and dimensions

Skyline is a technique in database management system for multi-criterion decision making based on dominance analysis. Skyline overcomes the limitation of relational databases by handling the criteria that are inversely proportional to each other. Traditional skyline operation is conceptualized over two dimensions only, and it finds out single interesting point. In this paper we extend the capability of skyline to work with multiple dimensions and to search the multiple interesting points from the given search space. The work furthermore ranks skyline points with respect to the multiple interesting points. However, we restrict the computational complexity within a fixed upper bound. Skyline is commonly applied on tourism industries, and we consider two different case studies from this domain and execute the proposed methodology over the real-life data. Comparative study is given based on different parameters, and statistical analysis is also performed to illustrate the efficacy of the proposed method over the existing methods.

Optimization of Dominance Testing in Skyline Queries Using Decision Trees

Skyline queries identify skyline points, the minimal set of data points that dominate all other data points in a large dataset. The main challenge with skyline queries is executing the skyline query in the shortest possible time. To address and solve skyline query performance issues, we propose a decision tree-based method known as the decision tree-based comparator (DC). This method minimizes unnecessary dominance tests (i.e., pairwise comparisons) by constructing a decision tree based on the dominance testing. DC uses dominance relations that can be obtained from the decision rules of the decision tree to determine incomparability between data points. DC can also be easily applied to improve the performance of various existing skyline query methods. After describing the theoretical background of DC and applying it to existing skyline queries, we present the results of various experiments showing that DC can improve skyline query performance by up to 23.15 times.

Efficient and Privacy-Preserving Multi-Party Skyline Queries Over Encrypted Data

One existing challenge associated with large scale skyline queries on cloud services, particularly when dealing with private information such as biomedical data, is supporting multi-party queries with curious-but-honest parties on encrypted data. In addition, existing solutions designed for performing secure skyline queries incur significant communication and computation costs due to ciphertext calculation. Thus, in this paper, we demonstrate the potential of supporting privacy-preserving multi-party skyline queries on encrypted data using additive homomorphic and proxy re-encryption cryptosystems. However, the secure computation based on these cryptosystems will further slow down query efficiency. To improve the efficiency of comparison on encrypted data, we redesign two lightweight secure comparison protocols. Meanwhile, we present an efficient method named “blind-reading” to securely obtain the skyline point. We also propose a novel method, Privacy Matrix, designed to reduce the scale of the dataset so that the computational cost is significantly decreased without privacy leakage. Then, we construct our secure skyline query protocol by integrating lightweight secure comparison protocols, “blind-reading” and Privacy Matrix techniques. Finally, we evaluate the security of our protocol, where we show it is secure without leaking information. The performance evaluation also shows that our proposed approach significantly improves the efficiency (at least $\times 4.5$ faster) compared to the-state-of-art and has the scalability of query processing under large datasets.

Speed and Direction Aware Skyline Query for Moving Objects

The skyline query is one of the most important supporting technologies for the location-based query services in the road network. Usually, when a user queries the skyline points in the road network, the query area is a user-centered circle or rectangle area, without considering the impact of the current movement speed and direction of the user on the formation of the query area. In this context, a speed and direction aware skyline query method is proposed, which can provide the skyline query area for the users by considering their moving speed and direction. Since the efficiency to directly obtain points of interest from speed and direction aware query area is not high, a Voronoi based speed and direction query area generation algorithm is proposed to approximate the query area, so as to improve the obtaining efficiency of points of interest in the area. The experiments on road networks and points of interest data of Beijing show the performance of the proposed method in terms of query efficiency and quality.

K-dominant Skyline query algorithm for dynamic datasets

At present, most k-dominant Skyline query algorithms are oriented to static datasets, this paper proposes a k-dominant Skyline query algorithm for dynamic datasets. The algorithm is recursive circularly. First, we compute the dominant ability of each object and sort objects in descending order by dominant ability. Then, we maintain an inverted index of the dominant index by k-dominant Skyline point calculation algorithm. When the data changes, it is judged whether the update point will affect the k-dominant Skyline point set. So the k-dominant Skyline point of the new data set is obtained by inserting and deleting algorithm. The proposed algorithm resolves maintenance issue of a frequently updated database by dynamically updating the data sets. The experimental results show that the query algorithm can effectively improve query efficiency.

Computation of spatial skyline points

The database skyline query (or non-domination query) has a spatial form: Given a set P with n point sites, and a point set S of m locations of interest, a site p∈P is a skyline point if and only if for each q∈P∖{p}, there exists at least one location s∈S that is closer to p than to q. We reduce the problem of determining skyline points to the problem of finding sites that have non-empty cells in an additively weighted Voronoi diagram under a convex distance function. The weights of said Voronoi diagram are derived from the coordinates of the sites of P, while the convex distance function is derived from the set of locations S. In the two-dimensional plane, this reduction gives an O((n+m)log⁡(n+m))-time algorithm to find the skyline points.

Dynamic planar range skyline queries in log logarithmic expected time

The skyline of a set P of points consists of the “best” points with respect to minimization or maximization of the attribute values. A point p dominates another point q if p is as good as q in all dimensions and it is strictly better than q in at least one dimension. In this work, we focus on the 2-d space and provide expected performance guarantees for dynamic (insertions and deletions) 3-sided range skyline queries. We assume that the x and y coordinates of the points are drawn from a class of distributions and present the ML-tree (Modified Layered Range-tree), which attains O(log2⁡Nlog⁡log⁡N) expected update time and O(tlog⁡log⁡N) time with high probability for finding planar skyline points in a 3-sided query rectangle q=[a,b]×[d,+∞) in the RAM model, where N is the cardinality of P and t is the answer size.

Researching Why-Not Questions in Skyline Query Based on Orthogonal Range

This paper aims to answer “why-not” questions in skyline queries based on the orthogonal query range (i.e., ORSQ). These queries retrieve skyline points within a rectangular query range, which improves query efficiency. Answering why-not questions in ORSQ can help users analyze query results and make decisions. We discuss the causes of why-not questions in ORSQ. Then, we outline how to modify the why-not point and the orthogonal query range so that the why-not point is included in the result of the skyline query based on the orthogonal range. When the why-not point is in the orthogonal range, we show how to modify the why-not point and narrow the orthogonal range. We also present how to expand the orthogonal range when the why-not point is not in the orthogonal range. We effectively combine query refinement and data modification techniques to produce meaningful answers. The experimental results demonstrate that the proposed algorithms have high-quality explanations for why-not questions in ORSQ in the real and synthetic datasets.

Group-Based Skyline for Pareto Optimal Groups

Skyline computation, aiming at identifying a set of skyline points that are not dominated by any other point, is particularly useful for multi-criteria data analysis and decision making. Traditional skyline computation, however, is inadequate to answer queries that need to analyze not only individual points but also groups of points. To address this gap, we generalize the original skyline definition to the novel group-based skyline (G-Skyline), which represents Pareto optimal groups that are not dominated by other groups. In order to compute G-Skyline groups consisting of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> points efficiently, we present a novel structure that represents the points in a directed skyline graph and captures the dominance relationships among the points based on the first <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> skyline layers. We propose efficient algorithms to compute the first <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> skyline layers. We then present two heuristic algorithms to efficiently compute the G-Skyline groups: the point-wise algorithm and the unit group-wise algorithm, using various pruning strategies. We observe that the number of G-Skyline groups of a dataset can be significantly large, we further propose the top- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> representative G-Skyline groups based on the number of dominated points and the number of dominated groups and present efficient algorithms for computing them. The experimental results on the real NBA dataset and the synthetic datasets show that G-Skyline is interesting and useful, and our algorithms are efficient and scalable.

Nearest and farthest spatial skyline queries under multiplicative weighted Euclidean distances

Consider two point sets in the plane, a set of points of interest and a set of query points that is used to establish distance restrictions with respect to the set of points of interest. A nearest/farthest spatial skyline query retrieves the subset of desirable or relevant points of interest, called skyline points, such that no other point of interest is simultaneously closer to/farther from all the query points. The nearest/farthest top-k spatial skylines, are the best k nearest/farthest spatial skylines among the existent ones. All these queries find applications in decision-making support systems, facility location, crisis management and in trips or events planning. To take into account that each point of interest has a different importance, a weight is assigned to each of them and multiplicative weighted Euclidean distances are used. In this paper, we study, for the first time, the nearest and farthest spatial skyline queries when multiplicative weighted Euclidean distances are considered. We prove that most of the properties of the traditional non weighted nearest and farthest spatial skyline queries are no longer true under the weighted Euclidean distance and, consequently, the strategies used for solving non weighted spatial skyline queries are not usable in the weighted case. We present a sequential and a parallel algorithm, to be run on the CPU and on a Graphics Processing Unit, respectively, for solving nearest/farthest weighted spatial skyline queries and to extract the nearest/farthest top-k spatial skylines. We provide the time and space complexity analysis of both algorithms together with their theoretical comparison. We also have developed a simple interface to deal with weighted spatial skyline queries which allows to visualize and store in a file the obtained spatial skylines. Finally, we present and discuss experimental results obtained with the implementation of the proposed sequential and parallel algorithms.

User Preference Analysis for Most Frequent Peer/Dominator

Given a set of objects $O$O (such as hotels), each can be represented as a point in a multi-dimensional feature space where each dimension corresponds to one attribute of the objects (such as price). Given the preference of a customer, the objects in $O$O not dominated by any other object (i.e., beat in all dimensions) are those worthy to be further considered. Such objects are known as skyline objects in database community. Suppose we have an object $o\in O$o∈O. If $o$o is a skyline point, other skyline objects are called peers of $o$o. If $o$o is not a skyline object, it must be dominated by some skyline objects which are called dominators of $o$o. Given a large number of user preferences, an interesting problem is to identify the most frequent peer/dominator (MFP/MFD) of $o$o. The MFP/MFD search has unique values in competitor analysis of various information systems. However, it is a challenging task because of the complexity to process a large number of user preferences. In this work, we provide robust solutions including exact and approximate methods. While the exact solutions explore the dominance relationship in the feature space, the approximate solutions are based on sampling techniques with theoretical bounds. We did extensive tests on large data sets which are up to 100 million user preferences generated from commercial surveys. The test resutls demonstrate the exact algorithms outperform various baseline algorithms significantly, and the approximate algorithms make further improvement by one order of magnitude with 90-98 percent accuracy.

Hierarchical Clustering Approach for Selecting Representative Skylines

Recently, the skyline query has attracted interest in a wide range of applications from recommendation systems to computer networks. The skyline query is useful to obtain the dominant data points from the given dataset. In the low-dimensional dataset, the skyline query may return a small number of skyline points. However, as the dimensionality of the dataset increases, the number of skyline points also increases. In other words, depending on the data distribution and dimensionality, most of the data points may become skyline points. With the emergence of big data applications, where the data distribution and dimensionality are a significant problem, obtaining representative skyline points among resulting skyline points is necessary. There have been several methods that focused on extracting representative skyline points with various success. However, existing methods have a problem of re-computation when the global threshold changes. Moreover, in certain cases, the resulting representative skyline points may not satisfy a user with multiple preferences. Thus, in this paper, we propose a new representative skyline query processing method, called representative skyline cluster (RSC), which solves the problems of the existing methods. Our method utilizes the hierarchical agglomerative clustering method to find the exact representative skyline points, which enable us to reduce the re-computation time significantly. We show the superiority of our proposed method over the existing state-of-the-art methods with various types of experiments.

Parallel k-dominant skyline queries in high-dimensional datasets

The skyline operator has been used to select preference points in many applications. The previously proposed k-dominant skyline, which relaxes the idea of dominance, reduces the number of skyline points in high-dimensional datasets. However, retrieving both skyline and k-dominant skyline points in high-dimensional datasets are computationally expensive. In this paper, we aim to consider all attributes simultaneously when retrieving skylines and k-dominant skyline points using a new data representation. Moreover, we propose a parallel k-dominant skyline algorithm, which obtains efficiency by exploring data parallelism. In the proposed algorithm, we introduce a data representation that significantly reduces the number of verifications between points and the computation of verifications. We implement the proposed algorithm on GPU frameworks, which are designed to perform data-parallel computation. For skyline queries, the experimental results show that the proposed algorithm outperforms the state-of-the-art GPU-based algorithms. In high dimensional space, the proposed algorithm is up to 10 times faster than the state-of-the-art GPU-based algorithm for skyline queries. We also evaluate and discuss the performance of the proposed algorithm for k-dominant skyline queries. With the proposed data representation, each point is averagely checked with less than 5% of points in k-dominant skyline queries, and 95% of verifications take only two comparisons.

Finding the informative and concise set through approximate skyline queries

Querying databases to search for “best” objects matching users’ preferences is a fundamental problem of intelligent systems and applications. The skyline query is an important tool for solving such a best-matching problem from the concept of multi-criteria optimization. However, it has the size problem as the size of the results of a skyline query grows superlinearly with the number of criteria. Here, we propose to find both the informative and concise set of skyline, a refined skyline set without similar objects. The informativeness requires the reduced set to cover the skyline, i.e., for every skyline point in the original dataset, there exists a close point in the reduced set, which help users to understand the skyline in more detail and make a better decision. The conciseness requires the size of the reduced set that can cover the skyline is as smaller as possible, which help users to make a quick decision. Finding both the informative and concise set of skyline will boost the usability of intelligent systems. More specifically, we propose two new skyline queries to find the informative and concise set of skyline: minimum skyline query, and extended minimum skyline query. The main idea is to return the minimum number of approximation objects, in which there is an object within a predefined distance threshold for each skyline object. The difference of the two query types is that the former one selects approximation objects only from skyline set, while the latter one selects from the whole dataset. We present an exact solution which computes minimum skyline in linear time for a 2d-space. As both minimum skyline and extended minimum skyline problems are NP-hard for dimensionality at least three, we present greedy solutions that obtain a 1+lnR approximation of the optimums. A comprehensive performance evaluation demonstrates that the size of skyline set can be effectively reduced by using the proposed (extended) minimum skyline queries and our proposed algorithms have promising results.

On fuzzy approaches for enlarging skyline query results

In the last decade, skyline queries have gained much attention and are proved to be valuable for multi-criteria decisions. Based on the concept of Pareto dominance, they return the non-dominated points, called the skyline points. In practice, it may happen that the skyline only contains a small number of points which could be insufficient for the user needs. In this paper, we discuss two fuzzy-set-based approaches to enriching the small skyline with particular points that could serve the decision makers’ needs. The basic idea consists in identifying the most interesting points among the non-skyline ones. On the one hand, we introduce a novel fuzzy dominance relationship which makes more demanding the dominance between the points of interest. So, much points would be considered as incomparable and then as elements of the new relaxed skyline. On the other hand, we leverage an appropriate fuzzy closeness relation to retrieve non skyline points that are fuzzily close to some skyline points. Furthermore, we develop efficient algorithms to compute the relaxed variants of skyline. Extensive experiments are conducted to demonstrate the effectiveness of our approaches and analyze the performance of the proposed algorithms. A comparative study between the approaches presented is made as well.

Finding the most influential product under distribution constraints through dominance tests

Market analysis is crucial for companies to remain invincible in the increasingly fierce market competition. A typical application is to find the most influential product, which attracts the largest number of customers, from a collection of candidate products. Previous work assumes a random distribution of the candidates. However, in many cases, there is a set of constraints on the distribution of candidate products. In this paper, we study the most influential product problem under constraints of the distribution. We model the constraints as both non-linear and linear constraints, where the candidate products reside in a hyper-rectangle and hyper-plane of the data space, respectively. We capitalize on reverse skyline queries to define the most influential product as the product with the largest reverse skyline set. We propose a general framework to solve the problem efficiently by taking advantage of candidate distributions. More specifically, we introduce a constraint-based filtering scheme, which prunes searching space and enables quick identification of some reverse skyline points, through pre-processing based on distribution constraints. We also propose a distance-based ordering technique, such that the processing results of a candidate can be utilized for data pruning of subsequent candidates. By combining the filtering scheme and ordering technique, we present two algorithms for handling different constraint models. Our experimental results with both real and synthetic datasets demonstrate the effectiveness and efficiency of our proposed algorithms.

Registration of Panoramic/Fish-Eye Image Sequence and LiDAR Points Using Skyline Features.

We propose utilizing a rigorous registration model and a skyline-based method for automatic registration of LiDAR points and a sequence of panoramic/fish-eye images in a mobile mapping system (MMS). This method can automatically optimize original registration parameters and avoid the use of manual interventions in control point-based registration methods. First, the rigorous registration model between the LiDAR points and the panoramic/fish-eye image was built. Second, skyline pixels from panoramic/fish-eye images and skyline points from the MMS’s LiDAR points were extracted, relying on the difference in the pixel values and the registration model, respectively. Third, a brute force optimization method was used to search for optimal matching parameters between skyline pixels and skyline points. In the experiments, the original registration method and the control point registration method were used to compare the accuracy of our method with a sequence of panoramic/fish-eye images. The result showed: (1) the panoramic/fish-eye image registration model is effective and can achieve high-precision registration of the image and the MMS’s LiDAR points; (2) the skyline-based registration method can automatically optimize the initial attitude parameters, realizing a high-precision registration of a panoramic/fish-eye image and the MMS’s LiDAR points; and (3) the attitude correction values of the sequences of panoramic/fish-eye images are different, and the values must be solved one by one.