Skyline Computation Research Articles

DTC-MDD: A spatiotemporal data acquisition technology for privacy-preserving in MCS

Some attackers in the Internet of Things submit falsified high-quality data to cause harm to users. To prevent malicious workers from reporting untruthful data for skyline computation in Mobile Crowd Sensing, we propose a double trust check-based spatiotemporal data acquisition scheme, DTC-MDD. In DTC-MDD, worker trust uses four-way validation to obtain reliable worker trust evaluations. Then, based on Probabilistic Skyline Calculation, we propose a worker selection algorithm to select high-trust, high-quality workers for data reporting. We also introduce the Non-Interactive Encrypted Integer Comparison Protocol to safeguard privacy between workers and users from malicious attacks. Finally, through extensive simulations on real datasets, DTC-MDD effectively enhances the quality and security of spatiotemporal data acquisition. DTC-MDD improved the data quality and reliability of candidate worker sets by 16.2% and 49.1%, respectively, and the data quality and reliability of the first skyline worker by 21.4% and 320.0%, respectively.

Efficient and privacy-preserving multi-party skyline queries in online medical primary diagnosis

Wireless body area networks enable data collection from wearable devices, thereby allowing online medical primary diagnosis via cloud computing. Data security and diagnosis accuracy are two main concerns in the online medical primary diagnosis system. While traditional solutions can ensure the confidentiality of online data, their incapacity to integrate data from multiple users restricts the development of accurate diagnostic models and leads to low accuracy. Recently, a medical preliminary diagnosis scheme with improved accuracy was proposed, which employs skyline computation to construct a precise diagnostic model using multiple medical datasets. However, their scheme requires a trusted third party and experiences excessive query time. To address this issue, we present an Effective and Privacy-preserving Multi-party Skyline diagnosis scheme (EPMS) that offers even higher accuracy and extremely fast diagnosis without trusted third parties. Specifically, we devise several sub-protocols to support secure skyline computation. By integrating our protocols with privacy matrix techniques, the cloud server can generate a comprehensive diagnostic model from multiple data sources, offering accurate diagnosis services without disclosing any users’ personal information. We implement our scheme and conduct extensive experiments, which showed that our approach achieves a speedup of approximately 200× in query time and nearly 20% improvement in accuracy.

Towards Efficient and Privacy-Preserving Interval Skyline Queries Over Time Series Data

Outsourcing encrypted time series data and query services to a cloud has been widely adopted by data owners for economic considerations. However, it inevitably lowers data utility and query efficiency. Existing secure skyline query schemes either leak critical information or are inefficient. In this paper, we propose an efficient and privacy-preserving interval skyline query scheme by employing symmetric homomorphic encryption (SHE). Specifically, we first devise a secure sort protocol to sort the encrypted dataset and a secure high-dimensional dominance check protocol to securely determine dominance relations of time series data, in which a dominance check tree is presented. With these secure protocols, we propose our secure skyline computation protocol that can ensure both security and efficiency. Furthermore, to deal with the characteristics of time series data, we design a look-up table to index time series for quick query response. The security analysis shows that our proposed scheme can protect outsourced data, query results, and single-dimensional privacy and hide access patterns. In addition, we evaluate our proposed scheme and compare the core component of our scheme with the state-of-the-art solution, and the results indicate that our protocol outperforms the compared solution by two orders of magnitude in the computational cost and at least 23× in the communication cost.

Dynamic Skyline Computation with LSD Trees

Given a set of high-dimensional feature vectors S⊂Rn, the skyline or Pareto problem is to report the subset of vectors in S that are not dominated by any vector of S. Vectors closer to the origin are preferred: we say a vector x is dominated by another distinct vector y if x is equally or further away from the origin than y with respect to all its dimensions. The dynamic skyline problem allows us to shift the origin, which changes the answer set. This problem is crucial for dynamic recommender systems where users can shift the parameters and thus shift the origin. For each origin shift, a recomputation of the answer set from scratch is time intensive. To tackle this problem, we propose a parallel algorithm for dynamic skyline computation that uses multiple local split decision (LSD) trees concurrently. The geometric nature of the LSD trees allows us to reuse previous results. Experiments show that our proposed algorithm works well if the dimension is small in relation to the number of tuples to process.

Skyline recomputation in Big Data

Retrieving relevant information in Big Data is a difficult task. Many approaches are used to select highly relevant information. One of them is the Skyline operator, which is used to select the best records in multidimensional data. The computation of the Skyline in large data or Big Data environments is highly expensive. Furthermore, updating the data requires a recomputation of the Skyline which leads to an exponential increase in the computation time. In this paper, we proposed a system that significantly reduces the computation time of the Skyline after updating the data. Our system uses the Skyline computation history to compute the new Skyline after the data is updated. We used in this system our proposed data representation and algorithms to handle the Skyline queries and the update queries. Based on the execution time, the experimental results show that the proposed system gives better results compared to existing approaches by keeping the Skyline Up to date.

SkyFlow: Heterogeneous streaming for skyline computation using FlowGraph and SYCL

The skyline is an optimization operator widely used for multi-criteria decision making. It allows minimizing an n-dimensional dataset into its smallest subset. In this work we present SkyFlow, the first heterogeneous CPU+GPU graph-based engine for skyline computation on a stream of data queries. Two data flow approaches, Coarse-grained and Fine-grained, have been proposed for different streaming scenarios. Coarse-grained aims to keep in parallel the computation of two queries using a hybrid solution with two state-of-the-art skyline algorithms: one optimized for CPU and another for GPU. We also propose a model to estimate at runtime the computation time of any arriving data query. This estimation is used by a heuristic to schedule the data query on the device queue in which it will finish earlier. On the other hand, Fine-grained splits one query computation between CPU and GPU. An experimental evaluation using as target architecture a heterogeneous system comprised of a multicore CPU and an integrated GPU for different streaming scenarios and datasets, reveals that our heterogeneous CPU+GPU approaches always outperform previous only-CPU and only-GPU state-of-the-art implementations up to 6.86×and 5.19×, respectively, and they fall below 6% of ideal peak performance at most. We also evaluate Coarse-grained vs Fine-Grained finding that each approach is better suited to different streaming scenarios.

Spatial-Keyword Skyline Publish/Subscribe Query Processing Over Distributed Sliding Window Streaming Data

Current spatial-keyword publish/subscribe systems need to handle spatial-keyword skyline queries over geo-textual streams to continuously obtain good results. The skyline queries in such systems face two main problems: (1) query problems, because the powerful query capability is required for the strict limit of the response time and the large number of items concerned by the users, and (2) scalability issue, because millions of active users are maintained simultaneously with many network-connected machines. Unfortunately, the current approach is towards static data. Thus, this paper first proposes a distributed skyline query processing framework. Then, we optimize the skyline computing by introducing MF-R <inline-formula><tex-math notation="LaTeX">$^t$</tex-math></inline-formula> -tree, which is an update-efficient and space-saving indexing structure and a fast approach for processing a continuous spatial-keyword skyline query called <inline-formula><tex-math notation="LaTeX">$eager^*$</tex-math></inline-formula> . Finally, a spatial and textual signature-based communication optimization method is proposed to support scalability. The experimental results indicate that (1) MF-R <inline-formula><tex-math notation="LaTeX">$^t$</tex-math></inline-formula> -tree can significantly reduce update costs, while maintaining a low storage cost, and a query performance comparable to IL-Quadtree, (2) <inline-formula><tex-math notation="LaTeX">$eager^*$</tex-math></inline-formula> can averagely accelerate 79.72 × faster than the method based on BNL, (3) the communication optimization method significantly reduces the communication cost, and (4) the distributed framework can efficiently support large-scale skyline queries.

A Continuous Region-Based Skyline Computation for a Group of Mobile Users

Skyline queries, which are based on the concept of Pareto dominance, filter the objects from a potentially large multi-dimensional collection of objects by keeping the best, most favoured objects in satisfying the user′s preferences. With today′s advancement of technology, ad hoc meetings or impromptu gatherings involving a group of people are becoming more and more common. Intuitively, deciding on an optimal meeting point is not a straightforward task especially when conflicting criteria are involved and the number of criteria to be considered is vast. Moreover, a point that is near to a user might not meet all the various users′ preferences, while a point that meets most of the users′ preferences might be located far away from these users. The task becomes more complicated when these users are on the move. In this paper, we present the Region-based Skyline for a Group of Mobile Users (RSGMU) method, which aims to resolve the problem of continuously finding the optimal meeting points, herein called skyline objects, for a group of users while they are on the move. RSGMU assumes a centroid-based movement where users are assumed to be moving towards a centroid that is identified based on the current locations of each user in the group. Meanwhile, to limit the searching space in identifying the objects of interest, a search region is constructed. However, the changes in the users′ locations caused the search region of the group to be reconstructed. Unlike the existing methods that require users to frequently report their latest locations, RSGMU utilises a dynamic motion formula, which abides to the laws of classical physics that are fundamentally symmetrical with respect to time, in order to predict the locations of the users at a specified time interval. As a result, the skyline objects are continuously updated, and the ideal meeting points can be decided upon ahead of time. Hence, the users′ locations as well as the spatial and non-spatial attributes of the objects are used as the skyline evaluation criteria. Meanwhile, to avoid re-computation of skylines at each time interval, the objects of interest within a Single Minimum Bounding Rectangle that is formed based on the current search region are organized in a Kd-tree data structure. Several experiments have been conducted and the results show that our proposed method outperforms the previous work with respect to CPU time.

Efficient Region-Based Skyline Computation for a Group of Users

Recently, with the advancement of technology, ad-hoc meetings or impromptu gathering are becoming more and more common. The meetings/gatherings which involve at least two people will require a specific physical point location that is useful or interesting to them, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">point of interest (PoI)</i> . These people might be residing at different locations; each with their own preferences which most likely to be different. Undoubtedly, given <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> people in a group, there will be <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> user’f preferences. Finding a suitable <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PoI</i> that meets these <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> user’f preferences is not a straightforward task. Existing solutions that utilise skyline processing in discovering the best, most preferred objects in satisfying the preferences of a group of users within a predetermined area have shown acceptable results. However, these solutions have to be executed repeatedly for each group of user’s queries since they do not exploit the possibilities that an area that has been visited by a group of users might be the area of interest of another group of users in the future. Inherently, they require rescanning the objects and recomputing the skylines of a previously visited region which is undoubtedly unwise and costly. This paper proposes the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Region-based Skyline for a Group of Users (RSGU)</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Extended Region-based Skyline for a Group of Users (ERSGU)</i> frameworks which attempt to resolve the limitations of existing solutions. In this work, skylines objects are point of interests ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PoIs</i> ) that are recommended to a group of users that are derived by analysing both the locations of the users, i.e. spatial attributes, as well as the spatial and non-spatial attributes of objects that are within a predetermined region of the group of users. Here, each region is partitioned into smaller units called fragments in such a way that overlapping areas between the currently and previously visited regions can be easily determined; while the results of computing the skylines of each fragment, known as fragment skylines, are saved to be utilised by the subsequent requests. Meanwhile, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ERSGU</i> has an additional feature in which the skylines derived for a group of users are not only based on the evaluation of the spatial and non-spatial attributes of the objects, but also the closeness of the objects to the desirable facilities or other interesting objects in the region. Undeniably, a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PoI</i> that is nearby to other attractions is appealing and worth the journey. Several experiments have been conducted and the results show that our proposed frameworks outperform the previous work with respect to CPU time.

IQSrec: An Efficient and Diversified Skyline Services Recommendation on Incomplete QoS

Recent developments of Internet technologies have accelerated the growth of Web services (<i>e.g.</i>, open APIs). As many services provide similar functionality, service recommendation systems use the Quality of Service (QoS) to help users find optimal services. Space partition attracts significant attention in service recommendation since it improves the diversity of recommendations and accelerates skyline services query. However, existing partition-based service recommendation systems are all implemented on complete QoS. They are not sufficient when some services&#x2019; QoS values are missing or invalid. To this end, we develop a new partition-based service recommendation method on incomplete QoS (named IQSrec) that combines probabilistic skyline query and space partition. The probabilistic skyline query measures top-<inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> skyline services on incomplete QoS. A dimension-based partition is specially designed for splitting the incomplete QoS service space into <inline-formula><tex-math notation="LaTeX">$d$</tex-math></inline-formula>-dimensional partitions with the most representative services. The candidate skyline services are chosen from each partition and merged together for probabilistic skyline computation. IQSrec selects the highest skyline probability services in each partition as recommendations. The experiments on the synthetic and real-world datasets show IQSrec can efficiently recommend skyline services on incomplete QoS. IQSrec has higher accuracy and diversity compared to the state-of-the-art service recommendation approaches.

Skyline refinement exploiting fuzzy formal concept analysis

PurposeThe study of the skyline queries has received considerable attention from several database researchers since the end of 2000's. Skyline queries are an appropriate tool that can help users to make intelligent decisions in the presence of multidimensional data when different, and often contradictory criteria are to be taken into account. Based on the concept of Pareto dominance, the skyline process extracts the most interesting (not dominated in the sense of Pareto) objects from a set of data. Skyline computation methods often lead to a set with a large size which is less informative for the end users and not easy to be exploited. The purpose of this paper is to tackle this problem, known as the large size skyline problem, and propose a solution to deal with it by applying an appropriate refining process.Design/methodology/approachThe problem of the skyline refinement is formalized in the fuzzy formal concept analysis setting. Then, an ideal fuzzy formal concept is computed in the sense of some particular defined criteria. By leveraging the elements of this ideal concept, one can reduce the size of the computed Skyline.FindingsAn appropriate and rational solution is discussed for the problem of interest. Then, a tool, named SkyRef, is developed. Rich experiments are done using this tool on both synthetic and real datasets.Research limitations/implicationsThe authors have conducted experiments on synthetic and some real datasets to show the effectiveness of the proposed approaches. However, thorough experiments on large-scale real datasets are highly desirable to show the behavior of the tool with respect to the performance and time execution criteria.Practical implicationsThe tool developed SkyRef can have many domains applications that require decision-making, personalized recommendation and where the size of skyline has to be reduced. In particular, SkyRef can be used in several real-world applications such as economic, security, medicine and services.Social implicationsThis work can be expected in all domains that require decision-making like hotel finder, restaurant recommender, recruitment of candidates, etc.Originality/valueThis study mixes two research fields artificial intelligence (i.e. formal concept analysis) and databases (i.e. skyline queries). The key elements of the solution proposed for the skyline refinement problem are borrowed from the fuzzy formal concept analysis which makes it clearer and rational, semantically speaking. On the other hand, this study opens the door for using the formal concept analysis and its extensions in solving other issues related to skyline queries, such as relaxation.

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.

Efficient Skyline Computation Over an Incomplete Database With Changing States and Structures

Skyline query has been studied extensively and a significant number of skyline algorithms have been proposed, mostly attempt to resolve the optimisation problem that is mainly associated with reduction in the processing time of skyline computations. While databases change their states and/or structures throughout their lifetime to reflect the current and latest information of the applications, the skyline set derived before changes are made towards the initial state of a database is no longer valid in the new state/structure of the database. The domination relationships between objects identified in the initial state might no longer hold in the new state. Nonetheless, computing the skylines over the entire new state/structure of the database is inefficient, as not all pairwise comparisons between the objects are necessary to be performed. In tackling the above issue, this paper proposes a solution, named Δ Skyline, which aims at avoiding unnecessary skyline computations when a database changes its state and structure due to a data definition operation(s) (add or remove a dimension(s)). This is achieved by identifying and retaining the prominent dominance relationships when pairwise comparisons are performed; which are then utilised in the process of computing a new skyline set. Δ Skyline consists of two optimisation components, namely: Δ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> Skyline which derives a new skyline set when a new dimension(s) is added to a database and Δ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sup> Skyline which derives a new skyline set when an existing dimension(s) is removed from a database. To make our solution more useful, it is applied on a database with incomplete data. Extensive experiments have been conducted to evaluate the performance and prove the efficiency of our proposed solution.

SecSky: A Secure Dynamic Skyline Query Scheme With Data Privacy

Skyline computation is a typical multi-objective optimization problem and has been a hot spot for current research. Most of them have concentrated on improving the efficiency of skyline computing, while the security issues associated with executing skyline computation in the cloud server are rarely taken into account. The cloud data stored in plaintext form is attacked by hackers or malicious administrators, resulting in potential leakage of users’ private information. One of the most effective approaches to solve this problem is to encrypt the private data before storing it in the cloud server. However, how to compute the skyline on the encrypted data stored on a cloud server efficiently is still challenging. In this paper, we present a novel framework called SecSky. Firstly, the improved B+ tree structure and symmetric encryption were combined to construct a secure storage structure. Then, the pruning idea was applied to reduce unnecessary calculation and to achieve efficient skyline query and dynamic update. The whole process was directly completed on the ciphertext data. Finally, both the security and the efficiency of SecSky were analyzed through theoretical proof and simulation experiments. The results showed that our scheme is of sound efficiency on the premise of ensuring private data security.

Secure and Efficient Probabilistic Skyline Computation for Worker Selection in MCS

The rapid advance of the Internet of Things (IoT) has enabled a new paradigm of the sensing network, i.e., mobile crowdsensing (MCS). Primarily, in MCS systems, a crowd of participating mobile users, namely, workers, are allocated by the MCS platforms to outsource their sensory data for specific tasks. Obviously, the reliability of workers and the trustability of their sensing data play significant roles in the service quality, thus the worker selection becomes crucial for the success of MCS applications. However, due to either a large number of candidates or their dynamic natures, selecting reliable workers poses big challenges to the MCS platform. Evidently, workers' reputation-based characteristics, such as trustability and credibility, are also pivotal for the worker selection in MCS, but they were often neglected in previous literature. In this article, aiming at addressing the above challenges, we propose a new privacy-preserving worker selection scheme based on the probabilistic skyline computation technique. Specifically, our proposed scheme is characterized by: 1) assigning a trustability score to each worker based on his/her past performance without revealing his/her sensitive information and 2) efficiently selecting a subset of reliable workers for a particular task. Detailed security analysis shows that our proposed scheme can preserve workers' privacy. In addition, performance evaluations via extensive simulations are conducted, and the results also demonstrate its effectiveness and efficiency for reliable worker selection in MCS applications.

Efficient Contour Computation of Group-Based Skyline

Skyline, aiming at finding a Pareto optimal subset of points in a multi-dimensional dataset, has gained great interest due to its extensive use for multi-criteria analysis and decision making. The skyline consists of all points that are not dominated by any other points. It is a candidate set of the optimal solution, which depends on a specific evaluation criterion for optimum. However, conventional skyline queries, which return individual points, are inadequate in group querying case since optimal combinations are required. To address this gap, we study the skyline computation in the group level and propose efficient methods to find the Group-based skyline (G-skyline). For computing the front $l$ skyline layers, we lay out an efficient approach that does the search concurrently on each dimension and investigates each point in the subspace. After that, we present a novel structure to construct the G-skyline with a queue of combinations of the first-layer points. We further demonstrate that the G-skyline is a complete candidate set of top-$l$ solutions, which is the main superiority over previous group-based skyline definitions. However, as G-skyline is complete, it contains a large number of groups which can make it impractical. To represent the "contour" of the G-skyline, we define the Representative G-skyline (RG-skyline). Then, we propose a Group-based clustering (G-clustering) algorithm to find out RG-skyline groups. Experimental results show that our algorithms are several orders of magnitude faster than the previous work.

Modeling and Computing Probabilistic Skyline on Incomplete Data

The skyline query is important in the database community. In recent years, the researches on incomplete data have been increasingly considered, especially for the skyline query. However, the existing skyline definition on incomplete data cannot provide users with valuable references. In this paper, we propose a novel skyline definition utilizing probabilistic model on incomplete data where each point has a probability to be in the skyline. In particular, it returns K points with the highest skyline probabilities. In addition, we propose incomplete models and estimate probability density functions of missing values on independent, correlated, and anti-correlated distributions, respectively. Meanwhile, it is a big challenge to compute probabilistic skyline on incomplete data. We propose three efficient algorithms SPISkyline, SPCSkyline, and SPASkyline for probabilistic skyline computation on incomplete data complying with independent, correlated, and anti-correlated distributions, respectively. They employ pruning strategy, optimization of the process of probability computation, and sorting technique to improve the efficiency of probabilistic skyline computation on incomplete data. Our experimental results demonstrate that our proposed concept of probabilistic skyline is an effective method to tackle skyline query on incomplete data and our algorithms are tens of times faster than the naive algorithm on both synthetic and real datasets.

HI-Sky: Hash Index-Based Skyline Query Processing

The skyline query has recently attracted a considerable amount of research interest in several fields. The query conducts computations using the domination test, where “domination” means that a data point does not have a worse value than others in any dimension, and has a better value in at least one dimension. Therefore, the skyline query can be used to construct efficient queries based on data from a variety of fields. However, when the number of dimensions or the amount of data increases, naïve skyline queries lead to a degradation in overall performance owing to the higher cost of comparisons among data. Several methods using index structures have been proposed to solve this problem but have not improved the performance of skyline queries because their indices are heavily influenced by the dimensionality and data amount. Therefore, in this study, we propose HI-Sky, a method that can perform quick skyline computations by using the hash index to overcome the above shortcomings. HI-Sky effectively manages data through the hash index and significantly improves performance by effectively eliminating unnecessary data comparisons when computing the skyline. We provide the theoretical background for HI-Sky and verify its improvement in skyline query performance through comparisons with prevalent methods.

Efficient Computation of Skyline Queries Over a Dynamic and Incomplete Database

Skyline queries rely on the notion of Pareto dominance, filter the data items by keeping only those data items that are the best, most preferred, also known as skylines, from a database to meet the user’s preferences. Skyline query has been studied extensively and a significant number of skyline algorithms have been proposed, mostly attempt to resolve the optimisation problem that is mainly associated with a reduction in the processing time of skyline computations. In today’s era, the presence of incomplete data in a database is inevitable. Furthermore, databases are dynamic in nature in which their states change throughout the time to reflect the current and latest information of the applications. The skylines derived before changes are made towards the initial database are no longer valid in the new state of the database. Blindly examining the entire database to identify the new set of skylines is unwise as not all data items are affected by the changes made towards the database. Hence, in this paper we propose a solution, named DyIn-Skyline , which is capable of deriving skylines over a dynamic and incomplete database, by exploiting only those data items that are affected by the changes. Several experiments have been conducted and the results show that our proposed solution outperforms the previous works with regard to the number of pairwise comparisons and processing time.

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.