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Graph matching, the problem of aligning a pair of graphs so as to minimize their edge disagreements, has received widespread attention owing to its broad spectrum of applications in data science. As the problem is NP–hard in the worst-case, a variety of approximation algorithms have been proposed for obtaining high quality, suboptimal solutions. In this article, we approach the task of designing an efficient polynomial-time approximation algorithm for graph matching from a previously unconsidered perspective. Our key result is that graph matching can be formulated as maximizing a monotone, supermodular set function subject to matroid intersection constraints. We leverage this fact to apply a discrete optimization variant of the minorization-maximization algorithm which exploits supermodularity of the objective function to iteratively construct and maximize a sequence of global lower bounds on the objective. At each step, we solve a maximum weight matching problem in a bipartite graph. Differing from prior approaches, the algorithm exploits the combinatorial structure inherent in the problem to generate a sequence of iterates featuring monotonically non-decreasing objective value while always adhering to the combinatorial matching constraints. Experiments on real-world data demonstrate the empirical effectiveness of the algorithm relative to the prevailing state-of-the-art. [ABSTRACT FROM AUTHOR]

Travel planning and recommendation are important aspects of transportation. We propose and investigate a novel Collective Travel Planning (CTP) query that finds the lowest-cost route connecting multiple sources and a destination, via at most $k$ meeting points. When multiple travelers target the same destination (e.g., a stadium or a theater), they may want to assemble at meeting points and then go together to the destination by public transport to reduce their global travel cost (e.g., energy, money, or greenhouse-gas emissions). This type of functionality holds the potential to bring significant benefits to society and the environment, such as reducing energy consumption and greenhouse-gas emissions, enabling smarter and greener transportation, and reducing traffic congestions. The CTP query is Max SNP-hard. To compute the query efficiently, we develop two algorithms, including an exact algorithm and an approximation algorithm. The exact algorithm is capable finding the optimal result for small values of $k$ (e.g., $k = 2$ ) in interactive time, while the approximation algorithm, which has a $5$ -approximation ratio, is suitable for other situations. The performance of the CTP query is studied experimentally with real and synthetic spatial data. [ABSTRACT FROM PUBLISHER]

Keyword-based search in text-rich multi-dimensional datasets facilitates many novel applications and tools. In this paper, we consider objects that are tagged with keywords and are embedded in a vector space. For these datasets, we study queries that ask for the tightest groups of points satisfying a given set of keywords. We propose a novel method called ProMiSH (Projection and Multi Scale Hashing) that uses random projection and hash-based index structures, and achieves high scalability and speedup. We present an exact and an approximate version of the algorithm. Our experimental results on real and synthetic datasets show that ProMiSH has up to 60 times of speedup over state-of-the-art tree-based techniques. [ABSTRACT FROM PUBLISHER]

Answering queries using views has proven effective for querying relational and semistructured data. This paper investigates this issue for graph pattern queries based on graph simulation. We propose a notion of pattern containment to characterize graph pattern matching using graph pattern views. We show that a pattern query can be answered using a set of views if and only if it is contained in the views. Based on this characterization, we develop efficient algorithms to answer graph pattern queries. We also study problems for determining (minimal, minimum) containment of pattern queries. We establish their complexity (from cubic-time to NP-complete) and provide efficient checking algorithms (approximation when the problem is intractable). In addition, when a pattern query is not contained in the views, we study maximally contained rewriting to find approximate answers; we show that it is in cubic-time to compute such rewriting, and present a rewriting algorithm. We experimentally verify that these methods are able to efficiently answer pattern queries on large real-world graphs. [ABSTRACT FROM AUTHOR]

Studies show that a person is willing to join a social group activity if the activity is interesting, and if some close friends also join the activity as companions. The literature has demonstrated that the interests of a person and the social tightness among friends can be effectively derived and mined from social networking websites. However, even with the above two kinds of information widely available, social group activities still need to be coordinated manually, and the process is tedious and time-consuming for users, especially for a large social group activity, due to complications of social connectivity and the diversity of possible interests among friends. To address the above important need, this paper proposes to automatically select and recommend potential attendees of a social group activity, which could be very useful for social networking websites as a value-added service. We first formulate a new problem, named Willingness mAximization for Social grOup (WASO). This paper points out that the solution obtained by a greedy algorithm is likely to be trapped in a local optimal solution. Thus, we design a new randomized algorithm to effectively and efficiently solve the problem. Given the available computational budgets, the proposed algorithm is able to optimally allocate the resources and find a solution with an approximation ratio. We implement the proposed algorithm in Facebook, and the user study demonstrates that social groups obtained by the proposed algorithm significantly outperform the solutions manually configured by users. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of identifying all locations of subtrees in a large tree or in a large collection of trees that are similar to a specified pattern tree, where all trees are assumed to be rooted and node-labeled. The tree edit distance is a widely-used measure of tree (dis-)similarity, but is NP-hard to compute for unordered trees. To cope with this issue, we propose a new similarity measure which extends the concept of unordered tree inclusion by taking the costs of insertion and substitution operations on the pattern tree into account, and present an algorithm for computing it. Our algorithm has the same time complexity as the original one for unordered tree inclusion, i.e., it runs in $O(T_1T_2)$ time, where $T_1$ and $T_2$ denote the pattern tree and the text tree, respectively, when the maximum outdegree of $T_1$ is bounded by a constant. Our experimental evaluation using synthetic and real datasets confirms that the proposed algorithm is fast and scalable and very useful for bibliographic matching, which is a typical entity resolution problem for tree-structured data. Furthermore, we extend our algorithm to also allow a constant number of deletion operations on $T_1$ while still running in $O(T_1T_2)$ time. [ABSTRACT FROM AUTHOR]

Influence maximization, defined as finding a small subset of nodes that maximizes spread of influence in social networks, is NP-hard under both Independent Cascade (IC) and Linear Threshold (LT) models, where many greedy-based algorithms have been proposed with the best approximation guarantee. However, existing greedy-based algorithms are inefficient on large networks, as it demands heavy Monte-Carlo simulations of the spread functions for each node at the initial step [7]. In this paper, we establish new upper bounds to significantly reduce the number of Monte-Carlo simulations in greedy-based algorithms, especially at the initial step. We theoretically prove that the bound is tight and convergent when the summation of weights towards (or from) each node is less than 1. Based on the bound, we propose a new Upper Bound based Lazy Forward algorithm ( UBLF in short) for discovering the top-k influential nodes in social networks. We test and compare UBLF with prior greedy algorithms, especially CELF [30]. Experimental results show that UBLF reduces more than 95 percent Monte-Carlo simulations of CELF and achieves about 2\-10 times speedup when the seed set is small. [ABSTRACT FROM PUBLISHER]

Graph datasets with billions of edges, such as social and web graphs, are prevalent, and scalability is critical. All-distances sketches (ADS) [Cohen 1997], are a powerful tool for scalable approximation of statistics. The sketch is a small size sample of the distance relation of a node which emphasizes closer nodes. Sketches for all nodes are computed using a nearly linear computation and estimators are applied to sketches of nodes to estimate their properties. We provide, for the first time, a unified exposition of ADS algorithms and applications. We present the historic inverse probability (HIP) estimators which are applied to the ADS of a node to estimate a large natural class of statistics. For the important special cases of neighborhood cardinalities (the number of nodes within some query distance) and closeness centralities, HIP estimators have at most half the variance of previous estimators and we show that this is essentially optimal. Moreover, HIP obtains a polynomial improvement for more general statistics and the estimators are simple, flexible, unbiased, and elegant. For approximate distinct counting on data streams, HIP outperforms the original estimators for the HyperLogLog MinHash sketches (Flajolet et al. 2007), obtaining significantly improved estimation quality for this state-of-the-art practical algorithm. [ABSTRACT FROM AUTHOR]

In time series analysis research, there is a strong interest in discrete representations of real valued data streams. One approach still considered state-of-the-art is the Symbolic Aggregate Approximation (SAX) algorithm. The interest of this paper concerns the SAX assumption of data being highly Gaussian and the use of the standard normal curve to choose partitions to discretize the data. The SAX approach chooses partitions on the standard normal curve that would produce an equal probability for each symbol. This procedure is generally valid as a time series is normalized to have $\mu = 0$ and $\sigma = 1$ . However, there exists a caveat to this assumption of equi-probability due to the intermediate step of Piecewise Aggregate Approximation (PAA). We show in this paper that when PAA is applied, the distribution of the data is altered, resulting in a shrinking standard deviation that is proportional to the number of points used to create a segment of the PAA representation and the degree of auto-correlation within the series. Data that exhibits statistically significant auto-correlation is less affected by this shrinking distribution. As the standard deviation of the data contracts, the mean remains the same, however the distribution is no longer standard normal and therefore the partitions based on the standard normal curve are no longer valid for the assumption of equal probability. [ABSTRACT FROM PUBLISHER]

Given the proliferation of review content, and the fact that reviews are highly diverse and often unnecessarily verbose, users frequently face the problem of selecting the appropriate reviews to consume. Micro-reviews are emerging as a new type of online review content in the social media. Micro-reviews are posted by users of check-in services such as Foursquare. They are concise (up to 200 characters long) and highly focused, in contrast to the comprehensive and verbose reviews. In this paper, we propose a novel mining problem, which brings together these two disparate sources of review content. Specifically, we use coverage of micro-reviews as an objective for selecting a set of reviews that cover efficiently the salient aspects of an entity. Our approach consists of a two-step process: matching review sentences to micro-reviews, and selecting a small set of reviews that cover as many micro-reviews as possible, with few sentences. We formulate this objective as a combinatorial optimization problem, and show how to derive an optimal solution using Integer Linear Programming. We also propose an efficient heuristic algorithm that approximates the optimal solution. Finally, we perform a detailed evaluation of all the steps of our methodology using data collected from Foursquare and Yelp. [ABSTRACT FROM PUBLISHER]

We consider simultaneously approximating all the columns of a data matrix in terms of few selected columns of another matrix that is sometimes called “the dictionary”. The challenge is to determine a small subset of the dictionary columns that can be used to obtain an accurate prediction of the entire data matrix. Previously proposed greedy algorithms for this task compare each data column with all dictionary columns, resulting in algorithms that may be too slow when both the data matrix and the dictionary matrix are large. A recent approach for accelerating the run time requires large amounts of memory to keep temporary values during the run of the algorithm. We propose two new algorithms that can be used even when both the data matrix and the dictionary matrix are large. The first algorithm is exact, with output identical to some previously proposed greedy algorithms. It takes significantly less memory when compared to the current state-of-the-art, and runs much faster when the dictionary matrix is sparse. The second algorithm uses a low rank approximation to the data matrix to further improve the run time. The algorithms use new recursive formulas for computing the greedy selection criterion. The formulas enable decoupling most of the computations related to the data matrix from the computations related to the dictionary matrix. [ABSTRACT FROM PUBLISHER]

As the volume of data grows at an unprecedented rate, large-scale data mining and knowledge discovery present a tremendous challenge. Rough set theory, which has been used successfully in solving problems in pattern recognition, machine learning, and data mining, centers around the idea that a set of distinct objects may be approximated via a lower and upper bound. In order to obtain the benefits that rough sets can provide for data mining and related tasks, efficient computation of these approximations is vital. The recently introduced cloud computing model, MapReduce, has gained a lot of attention from the scientific community for its applicability to large-scale data analysis. In previous research, we proposed a MapReduce-based method for computing approximations in parallel, which can efficiently process complete data but fails in the case of missing (incomplete) data. To address this shortcoming, three different parallel matrix-based methods are introduced to process large-scale, incomplete data. All of them are built on MapReduce and implemented on Twister that is a lightweight MapReduce runtime system. The proposed parallel methods are then experimentally shown to be efficient for processing large-scale data. [ABSTRACT FROM AUTHOR]

As machine learning techniques mature and are used to tackle complex scientific problems, challenges arise such as the imbalanced class distribution problem, where one of the target class labels is under-represented in comparison with other classes. Existing oversampling approaches for addressing this problem typically do not consider the probability distribution of the minority class while synthetically generating new samples. As a result, the minority class is not represented well which leads to high misclassification error. We introduce two probabilistic oversampling approaches, namely RACOG and wRACOG, to synthetically generating and strategically selecting new minority class samples. The proposed approaches use the joint probability distribution of data attributes and Gibbs sampling to generate new minority class samples. While RACOG selects samples produced by the Gibbs sampler based on a predefined lag, wRACOG selects those samples that have the highest probability of being misclassified by the existing learning model. We validate our approach using nine UCI data sets that were carefully modified to exhibit class imbalance and one new application domain data set with inherent extreme class imbalance. In addition, we compare the classification performance of the proposed methods with three other existing resampling techniques. [ABSTRACT FROM PUBLISHER]

Rule induction method based on rough set theory (RST) has received much attention recently since it may generate a minimal set of rules from the decision system for real-life applications by using of attribute reduction and approximations. The decision system may vary with time, e.g., the variation of objects, attributes and attribute values. The reduction and approximations of the decision system may alter on Attribute Values’ Coarsening and Refining (AVCR), a kind of variation of attribute values, which results in the alteration of decision rules simultaneously. This paper aims for dynamic maintenance of decision rules $w.r.t.$ AVCR. The definition of minimal discernibility attribute set is proposed firstly, which aims to improve the efficiency of attribute reduction in RST. Then, principles of updating decision rules in case of AVCR are discussed. Furthermore, the rough set-based methods for updating decision rules in the inconsistent decision system are proposed. The complexity analysis and extensive experiments on UCI data sets have verified the effectiveness and efficiency of the proposed methods. [ABSTRACT FROM PUBLISHER]

Users are often faced with the problem of finding complementary items that together achieve a single common goal (e.g., a starter kit for a novice astronomer, a collection of question/answers related to low-carb nutrition, a set of places to visit on holidays). In this paper, we argue that for some application scenarios returning item bundles is more appropriate than ranked lists. Thus we define composite retrieval as the problem of finding k bundles of complementary items. Beyond complementarity of items, the bundles must be valid w.r.t. a given budget, and the answer set of k bundles must exhibit diversity. We formally define the problem and show that in its general form is \bf NP-hard  and that also the special cases in which each bundle is formed by only one item, or only one bundle is sought, are hard. Our characterization however suggests how to adopt a two-phase approach (Produce-and-Choose, or PAC) in which we first produce many valid bundles, and then we choose k among them. For the first phase we devise two ad-hoc clustering algorithms, while for the second phase we adapt heuristics with approximation guarantees for a related problem. We also devise another approach which is based on first finding a k-clustering and then selecting a valid bundle from each of the produced clusters (Cluster-and-Pick, or CAP). We compare experimentally the proposed methods on two real-world data sets: the first data set is given by a sample of touristic attractions in 10 large European cities, while the second is a large database of user-generated restaurant reviews from Yahoo! Local. Our experiments show that when diversity is highly important, CAP is the best option, while when diversity is less important, a PAC approach constructing bundles around randomly chosen pivots, is better. [ABSTRACT FROM AUTHOR]

Majority of the existing works on network analysis study properties that are related to the global topology of a network. Examples of such properties include diameter, power-law exponent, and spectra of graph Laplacian. Such works enhance our understanding of real-life networks, or enable us to generate synthetic graphs with real-life graph properties. However, many of the existing problems on networks require the study of local topological structures of a network, which did not get the deserved attention in the existing works. In this work, we use graphlet frequency distribution (GFD) as an analysis tool for understanding the variance of local topological structure in a network; we also show that it can help in comparing, and characterizing real-life networks. The main bottleneck to obtain GFD is the excessive computation cost for obtaining the frequency of each of the graphlets in a large network. To overcome this, we propose a simple, yet powerful algorithm, called Graft , that obtains the approximate graphlet frequency for all graphlets that have up-to five vertices. Comparing to an exact counting algorithm, our algorithm achieves a speedup factor between 10 and 100 for a negligible counting error, which is, on average, less than 5 percent. [ABSTRACT FROM AUTHOR]

PageRank is one of the most commonly used techniques for ranking nodes in a network. It is a special case of a family of link-based rankings, commonly referred to as functional rankings. Functional rankings are computed as power series of a stochastic matrix derived from the adjacency matrix of the graph. This general formulation of functional rankings enables their use in diverse applications, ranging from traditional search applications to identification of spam and outliers in networks. This paper presents a novel algorithmic (re)formulation of commonly used functional rankings, such as LinearRank, TotalRank and Generalized Hyperbolic Rank. These rankings can be approximated by finite series representations. We prove that polynomials of stochastic matrices can be expressed as products of Google matrices (matrices having the form used in Google’s original PageRank formulation). Individual matrices in these products are parameterized by different damping factors. For this reason, we refer to our formulation as multidamping. We demonstrate that multidamping has a number of desirable characteristics: (i) for problems such as finding the highest ranked pages, multidamping admits extremely fast approximate solutions; (ii) multidamping provides an intuitive interpretation of existing functional rankings in terms of the surfing habits of model web users; (iii) multidamping provides a natural framework based on Monte Carlo type methods that have efficient parallel and distributed implementations. It also provides the basis for constructing new link-based rankings based on inhomogeneous products of Google matrices. We present algorithms for computing damping factors for existing functional rankings analytically and numerically. We validate various benefits of multidamping on a number of real datasets. [ABSTRACT FROM AUTHOR]

Frequent pattern mining often produces an enormous number of frequent patterns, which imposes a great challenge on visualizing, understanding and further analysis of the generated patterns. This calls for finding a small number of representative patterns to best approximate all other patterns. In this paper, we develop an algorithm called MinRPset to find a minimum representative pattern set with error guarantee. MinRPset produces the smallest solution that we can possibly have in practice under the given problem setting, and it takes a reasonable amount of time to finish when the number of frequent closed patterns is below one million. MinRPset is very space-consuming and time-consuming on some dense datasets when the number of frequent closed patterns is large. To solve this problem, we propose another algorithm called FlexRPset, which provides one extra parameter \(K\) to allow users to make a trade-off between result size and efficiency. We adopt an incremental approach to let the users make the trade-off conveniently. Our experiment results show that MinRPset and FlexRPset produce fewer representative patterns than RPlocal—an efficient algorithm that is developed for solving the same problem. [ABSTRACT FROM PUBLISHER]

The selection of relevant and significant features is an important problem particularly for data sets with large number of features. In this regard, a new feature selection algorithm is presented based on a rough hypercuboid approach. It selects a set of features from a data set by maximizing the relevance, dependency, and significance of the selected features. By introducing the concept of the hypercuboid equivalence partition matrix, a novel representation of degree of dependency of sample categories on features is proposed to measure the relevance, dependency, and significance of features in approximation spaces. The equivalence partition matrix also offers an efficient way to calculate many more quantitative measures to describe the inexactness of approximate classification. Several quantitative indices are introduced based on the rough hypercuboid approach for evaluating the performance of the proposed method. The superiority of the proposed method over other feature selection methods, in terms of computational complexity and classification accuracy, is established extensively on various real-life data sets of different sizes and dimensions. [ABSTRACT FROM AUTHOR]

GPS-enabled devices are pervasive nowadays. Finding movement patterns in trajectory data stream is gaining in importance. We propose a group discovery framework that aims to efficiently support the online discovery of moving objects that travel together. The framework adopts a sampling-independent approach that makes no assumptions about when positions are sampled, gives no special importance to sampling points, and naturally supports the use of approximate trajectories. The framework's algorithms exploit state-of-the-art, density-based clustering (DBScan) to identify groups. The groups are scored based on their cardinality and duration, and the top-$(k)$ groups are returned. To avoid returning similar subgroups in a result, notions of domination and similarity are introduced that enable the pruning of low-interest groups. Empirical studies on real and synthetic data sets offer insight into the effectiveness and efficiency of the proposed framework. [ABSTRACT FROM PUBLISHER]

Finding the appropriate number of clusters to which documents should be partitioned is crucial in document clustering. In this paper, we propose a novel approach, namely DPMFP, to discover the latent cluster structure based on the DPM model without requiring the number of clusters as input. Document features are automatically partitioned into two groups, in particular, discriminative words and nondiscriminative words, and contribute differently to document clustering. A variational inference algorithm is investigated to infer the document collection structure as well as the partition of document words at the same time. Our experiments indicate that our proposed approach performs well on the synthetic data set as well as real data sets. The comparison between our approach and state-of-the-art document clustering approaches shows that our approach is robust and effective for document clustering. [ABSTRACT FROM AUTHOR]

We study the problem of clustering probabilistic graphs. Similar to the problem of clustering standard graphs, probabilistic graph clustering has numerous applications, such as finding complexes in probabilistic protein-protein interaction (PPI) networks and discovering groups of users in affiliation networks. We extend the edit-distance-based definition of graph clustering to probabilistic graphs. We establish a connection between our objective function and correlation clustering to propose practical approximation algorithms for our problem. A benefit of our approach is that our objective function is parameter-free. Therefore, the number of clusters is part of the output. We also develop methods for testing the statistical significance of the output clustering and study the case of noisy clusterings. Using a real protein-protein interaction network and ground-truth data, we show that our methods discover the correct number of clusters and identify established protein relationships. Finally, we show the practicality of our techniques using a large social network of Yahoo! users consisting of one billion edges. [ABSTRACT FROM AUTHOR]

Approximations of a concept by a variable precision rough-set model (VPRS) usually vary under a dynamic information system environment. It is thus effective to carry out incremental updating approximations by utilizing previous data structures. This paper focuses on a new incremental method for updating approximations of VPRS while objects in the information system dynamically alter. It discusses properties of information granulation and approximations under the dynamic environment while objects in the universe evolve over time. The variation of an attribute's domain is also considered to perform incremental updating for approximations under VPRS. Finally, an extensive experimental evaluation validates the efficiency of the proposed method for dynamic maintenance of VPRS approximations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new type of Dictionary-based Entity Recognition Problem, named Approximate Membership Localization (AML). The popular Approximate Membership Extraction (AME) provides a full coverage to the true matched substrings from a given document, but many redundancies cause a low efficiency of the AME process and deteriorate the performance of real-world applications using the extracted substrings. The AML problem targets at locating nonoverlapped substrings which is a better approximation to the true matched substrings without generating overlapped redundancies. In order to perform AML efficiently, we propose the optimized algorithm P-Prune that prunes a large part of overlapped redundant matched substrings before generating them. Our study using several real-word data sets demonstrates the efficiency of P-Prune over a baseline method. We also study the AML in application to a proposed web-based join framework scenario which is a search-based approach joining two tables using dictionary-based entity recognition from web documents. The results not only prove the advantage of AML over AME, but also demonstrate the effectiveness of our search-based approach. [ABSTRACT FROM AUTHOR]

Attribute reduction is the strongest and most characteristic result in rough set theory to distinguish itself to other theories. In the framework of rough set, an approach of discernibility matrix and function is the theoretical foundation of finding reducts. In this paper, sample pair selection with rough set is proposed in order to compress the discernibility function of a decision table so that only minimal elements in the discernibility matrix are employed to find reducts. First relative discernibility relation of condition attribute is defined, indispensable and dispensable condition attributes are characterized by their relative discernibility relations and key sample pair set is defined for every condition attribute. With the key sample pair sets, all the sample pair selections can be found. Algorithms of computing one sample pair selection and finding reducts are also developed; comparisons with other methods of finding reducts are performed with several experiments which imply sample pair selection is effective as preprocessing step to find reducts. [ABSTRACT FROM PUBLISHER]

Traditional clustering techniques are inapplicable to problems where the relationships between data points evolve over time. Not only is it important for the clustering algorithm to adapt to the recent changes in the evolving data, but it also needs to take the historical relationship between the data points into consideration. In this paper, we propose ECKF, a general framework for evolutionary clustering large-scale data based on low-rank kernel matrix factorization. To the best of our knowledge, this is the first work that clusters large evolutionary data sets by the amalgamation of low-rank matrix approximation methods and matrix factorization-based clustering. Since the low-rank approximation provides a compact representation of the original matrix, and especially, the near-optimal low-rank approximation can preserve the sparsity of the original data, ECKF gains computational efficiency and hence is applicable to large evolutionary data sets. Moreover, matrix factorization-based methods have been shown to effectively cluster high-dimensional data in text mining and multimedia data analysis. From a theoretical standpoint, we mathematically prove the convergence and correctness of ECKF, and provide detailed analysis of its computational efficiency (both time and space). Through extensive experiments performed on synthetic and real data sets, we show that ECKF outperforms the existing methods in evolutionary clustering. [ABSTRACT FROM PUBLISHER]

Top-k dominating queries use an intuitive scoring function which ranks multidimensional points with respect to their dominance power, i.e., the number of points that a point dominates. The k points with the best (e.g., highest) scores are returned to the user. Both top-k and skyline queries have been studied in a streaming environment, where changes to the data set are very frequent. In such an environment, continuous query processing techniques are required toward efficient monitoring of query results, since periodic query re-execution is computationally intensive, and therefore, prohibitive. This work contains the first study of continuous top-k dominating queries over data streams. In comparison to continuous top-k and skyline queries, continuous top-k dominating queries pose additional challenges. Three exact algorithms (BFA, EVA, ADA) are studied, and among them ADA, which is enhanced with additional optimization techniques, shows the best overall performance. In some cases, we are willing to trade accuracy for speed. Toward this direction, two approximate algorithms are proposed (AHBA and AMSA). AHBA offers probabilistic guarantees regarding the accuracy of the result based on the Hoeffding bound, whereas AMSA performs a more aggressive computation resulting in more efficient processing. Evaluation results, based on real-life and synthetic data sets, show the efficiency and scalability of our techniques. [ABSTRACT FROM PUBLISHER]

Given a set of points P and a query set Q, a group enclosing query (Geq) fetches the point p* â P such that the maximum distance of p* to all points in Q is minimized. This problem is equivalent to the Min-Max case (minimizing the maximum distance) of aggregate nearest neighbor queries for spatial databases [27]. This work first designs a new exact solution by exploring new geometric insights, such as the minimum enclosing ball, the convex hull, and the furthest voronoi diagram of the query group. To further reduce the query cost, especially when the dimensionality increases, we turn to approximation algorithms. Our main approximation algorithm has a worst case \sqrt2-approximation ratio if one can find the exact nearest neighbor of a point. In practice, its approximation ratio never exceeds 1.05 for a large number of data sets up to six dimensions. We also discuss how to extend it to higher dimensions (up to 74 in our experiment) and show that it still maintains a very good approximation quality (still close to 1) and low query cost. In fixed dimensions, we extend the \sqrt2-approximation algorithm to get a (1 + ε)-approximate solution for the Geq problem. Both approximation algorithms have O(\log N + M) query cost in any fixed dimension, where N and M are the sizes of the data set P and query group Q. Extensive experiments on both synthetic and real data sets, up to 10 million points and 74 dimensions, confirm the efficiency, effectiveness, and scalability of the proposed algorithms, especially their significant improvement over the state-of-the-art method. [ABSTRACT FROM AUTHOR]

Authority flow and proximity search have been used extensively in measuring the association between entities in data graphs, ranging from the web to relational and XML databases. These two ranking factors have been used and studied separately in the past. In addition to their semantic differences, a key advantage of proximity search is the existence of efficient execution algorithms. In contrast, due to the complexity of calculating the authority flow, current systems only use precomputed authority flows in runtime. This limitation prohibits authority flow to be used more effectively as a ranking factor. In this paper, we present a comparative analysis of the two ranking factors. We present an efficient approximation of authority flow based on proximity search. We analytically estimate the approximation error and how this affects the ranking of the results of a query. [ABSTRACT FROM PUBLISHER]