Top-<Emphasis Type="Italic">k</Emphasis> probabilistic prevalent co-location mining in spatially uncertain data sets

A co-location pattern is a set of spatial features whose instances frequently appear in a spatial neighborhood. This paper efficiently mines the top-k probabilistic prevalent co-locations over spatially uncertain data sets and makes the following contributions: 1) the concept of the top-k probabilistic prevalent co-locations based on a possible world model is defined; 2) a framework for discovering the top-k probabilistic prevalent co-locations is set up; 3) a matrix method is proposed to improve the computation of the prevalence probability of a top-k candidate, and two pruning rules of the matrix block are given to accelerate the search for exact solutions; 4) a polynomial matrix is developed to further speed up the top-k candidate refinement process; 5) an approximate algorithm with compensation factor is introduced so that relatively large quantity of data can be processed quickly. The efficiency of our proposed algorithms as well as the accuracy of the approximation algorithms is evaluated with an extensive set of experiments using both synthetic and real uncertain data sets.     

Approximate Continuous Top-<Emphasis Type="Italic">k</Emphasis> Query over Sliding Window

Continuous top-k query over sliding window is a fundamental problem in database, which retrieves k objects with the highest scores when the window slides. Existing studies mainly adopt exact algorithms to tackle this type of queries, whose key idea is to maintain a subset of objects in the window, and try to retrieve answers from it. However, all the existing algorithms are sensitive to query parameters and data distribution. In addition, they suffer from expensive overhead for incremental maintenance, and thus cannot satisfy real-time requirement. In this paper, we define a novel query named (ε, δ)-approximate continuous top-k query, which returns approximate answers for top-k query. In order to efficiently support this query, we propose an efficient framework, named PABF (Probabilistic Approximate Based Framework), to support approximate top-k query over sliding window. We firstly maintain a self-adaptive pruning value, which could filter out newly arrived objects who have a probability less than 1 ? δ of being a query result. For those objects that are not filtered, we combine them together, if the score difference among them is less than a threshold. To efficiently maintain these combined results, the framework PABF also proposes a multi-phase merging algorithm. Theoretical analysis indicates that even in the worst case, we require only logarithmic complexity for maintaining each candidate.     

Scalable and efficient processing of top-<Emphasis Type="Italic">k</Emphasis> multiple-type integrated queries

In this paper, we define a new class of queries, the top-k multiple-type integrated query (simply, top-k MULTI query). It deals with multiple data types and finds the information in the order of relevance between the query and the object. Various data types such as spatial, textual, and relational data types can be used for the top-k MULTI query. The top-k MULTI query distinguishes itself from the traditional top-k query in that the component scores to calculate final scores are determined dependent of the query. Hence, each component score is calculated only when the query is given for each data type rather than being calculated apriori as in the top-k query. As a representative instance, the traditional top-k spatial keyword query is an instance of the top-k MULTI query. It deals with the spatial data type and text data type and finds the information based on spatial proximity and textual relevance between the query and the object, which is determined only when the query is given. In this paper, we first define the top-k MULTI query formally and define a new specific instance for the top-k MULTI query, the top-k spatial-keyword-relational(SKR) query, by integrating the relational data type into the traditional top-k spatial keyword query. Then, we investigate the processing approaches for the top-k MULTI query. We discuss the scalability of those approaches as new data types are integrated. We also devise the processing methods for the top-k SKR query. Finally, through extensive experiments on the top-k SKR query using real and synthetic data sets, we compare efficiency of the methods in terms of the query performance and storage.     

Answering why-not and why questions on reverse top-<Emphasis Type="Italic">k</Emphasis> queries

Why-not and why questions can be posed by database users to seek clarifications on unexpected query results. Specifically, why-not questions aim to explain why certain expected tuples are absent from the query results, while why questions try to clarify why certain unexpected tuples are present in the query results. This paper systematically explores the why-not and why questions on reverse top-k queries, owing to its importance in multi-criteria decision making. We first formalize why-not questions on reverse top-k queries, which try to include the missing objects in the reverse top-k query results, and then, we propose a unified framework called WQRTQ to answer why-not questions on reverse top-k queries. Our framework offers three solutions to cater for different application scenarios. Furthermore, we study why questions on reverse top-k queries, which aim to exclude the undesirable objects from the reverse top-k query results, and extend the framework WQRTQ to efficiently answer why questions on reverse top-k queries, which demonstrates the flexibility of our proposed algorithms. Extensive experimental evaluation with both real and synthetic data sets verifies the effectiveness and efficiency of the presented algorithms under various experimental settings.     

Uncertain top-<Emphasis Type="Italic">k</Emphasis> query processing in distributed environments

The top-k query on uncertain data set has been a very hot topic these years, and there have been many studies on uncertain top-k queries. Unfortunately, most of the existing algorithms only consider centralized processing environments, and they are not suitable for the large-scale data. In this paper, it is the first attempt to process probabilistic threshold top-k queries (an important uncertain top-k query, PT-k for short) in a distributed environment. We propose 3 efficient algorithms. The serial distributed approach adopts a new method, which only requires a few amount of calculations, to serially process PT-k queries in distributed environments. The global sorting first algorithm for PT-k query processing (GSP) is designed for improving the computation speed. In GSP, a distributed sorting operation is performed, and then we compute the candidates for PT-k queries in parallel. The query results can be computed by using a novel incremental method which can reduce the number of calculations. The local filtering first algorithm for PT-k query processing is designed for reducing the network overhead. Specifically, several filtering strategies are proposed to filter out redundant data locally, and then the incremental method in GSP is used to process the PT-k queries. Finally, the effectiveness of our proposed algorithms is verified through a series of experiments.     

Diversified top-<Emphasis Type="Italic">k</Emphasis> clique search

Maximal clique enumeration is a fundamental problem in graph theory and has been extensively studied. However, maximal clique enumeration is time-consuming in large graphs and always returns enormous cliques with large overlaps. Motivated by this, in this paper, we study the diversified top-k clique search problem which is to find top-k cliques that can cover most number of nodes in the graph. Diversified top-k clique search can be widely used in a lot of applications including community search, motif discovery, and anomaly detection in large graphs. A naive solution for diversified top-k clique search is to keep all maximal cliques in memory and then find k of them that cover most nodes in the graph by using the approximate greedy max k-cover algorithm. However, such a solution is impractical when the graph is large. In this paper, instead of keeping all maximal cliques in memory, we devise an algorithm to maintain k candidates in the process of maximal clique enumeration. Our algorithm has limited memory footprint and can achieve a guaranteed approximation ratio. We also introduce a novel light-weight \(\mathsf {PNP}\)-\(\mathsf {Index}\), based on which we design an optimal maximal clique maintenance algorithm. We further explore three optimization strategies to avoid enumerating all maximal cliques and thus largely reduce the computational cost. Besides, for the massive input graph, we develop an I/O efficient algorithm to tackle the problem when the input graph cannot fit in main memory. We conduct extensive performance studies on real graphs and synthetic graphs. One of the real graphs contains 1.02 billion edges. The results demonstrate the high efficiency and effectiveness of our approach.     

Top-<Emphasis Type="Italic">k</Emphasis> query processing in mobile-P2P networks using economic incentive schemes

This work proposes the E-Top system for the efficient processing of top-k queries in mobile ad hoc peer to peer (M-P2P) networks using economic incentive schemes. In E-Top, brokers facilitate top-k query processing in lieu of a commission. E-Top issues economic rewards to the mobile peers, which send relevant data items (i.e., those that contribute to the top-k query result), and penalizes peers otherwise, thereby optimizing the communication traffic. Peers use the payoffs (rewards/penalties) as a means of feedback to re-evaluate the scores of their items for re-ranking purposes. The main contributions of E-Top are three-fold. First, it proposes two economic incentive schemes, namely ETK and ETK+, in which peers act individually towards top-k query processing. Second, it extends ETK and ETK+ to propose a peer group-based economic incentive scheme ETG. Third, our performance evaluation shows that our schemes are indeed effective in improving the performance of top-k queries in terms of query response times and accuracy at reasonable communication traffic cost.     

An efficient algorithm for mining top-<Emphasis Type="Italic">k</Emphasis> on-shelf high utility itemsets

High on-shelf utility itemset (HOU) mining is an emerging data mining task which consists of discovering sets of items generating a high profit in transaction databases. The task of HOU mining is more difficult than traditional high utility itemset (HUI) mining, because it also considers the shelf time of items, and items having negative unit profits. HOU mining can be used to discover more useful and interesting patterns in real-life applications than traditional HUI mining. Several algorithms have been proposed for this task. However, a major drawback of these algorithms is that it is difficult for users to find a suitable value for the minimum utility threshold parameter. If the threshold is set too high, not enough patterns are found. And if the threshold is set too low, too many patterns will be found and the algorithm may use an excessive amount of time and memory. To address this issue, we propose to address the problem of top-k on-shelf high utility itemset mining, where the user directly specifies k, the desired number of patterns to be output instead of specifying a minimum utility threshold value. An efficient algorithm named KOSHU (fast top-K on-shelf high utility itemset miner) is proposed to mine the top-k HOUs efficiently, while considering on-shelf time periods of items, and items having positive and/or negative unit profits. KOSHU introduces three novel strategies, named efficient estimated co-occurrence maximum period rate pruning, period utility pruning and concurrence existing of a pair 2-itemset pruning to reduce the search space. KOSHU also incorporates several novel optimizations and a faster method for constructing utility-lists. An extensive performance study on real-life and synthetic datasets shows that the proposed algorithm is efficient both in terms of runtime and memory consumption and has excellent scalability.     

Prefix-projection global constraint and top-<Emphasis Type="Italic">k</Emphasis> approach for sequential pattern mining

Sequential pattern mining (SPM) is an important data mining problem with broad applications. SPM is a hard problem due to the huge number of intermediate subsequences to be considered. State of the art approaches for SPM (e.g., PrefixSpan Pei et al. 2001) are largely based on the pattern-growth approach, where for each frequent prefix subsequence, only its related suffix subsequences need to be considered, and the database is recursively projected into smaller ones. Many authors have promoted the use of constraints to focus on the most promising patterns according to the interests of the end user. The top-k SPM problem is also used to cope with the difficulty of thresholding and to control the number of solutions. State of the art methods developed for SPM and top-k SPM, though efficient, are locked into a rather rigid search strategy, and suffer from the lack of declarativity and flexibility. Indeed, adding new constraints usually amounts to changing the data-structures used in the core of the algorithm, and combining these new constraints often require new developments. Recent works (e.g. Kemmar et al. 2014; Négrevergne and Guns 2015) have investigated the use of Constraint Programming (CP) for SPM. However, despite their nice declarative aspects, all these modelings have scaling problems, due to the huge size of their constraint networks. To address this issue, we propose the Prefix-Projection global constraint, which encapsulates both the subsequence relation as well as the frequency constraint. Its filtering algorithm relies on the principle of projected databases which allows to keep in the variables domain, only values leading to a frequent pattern in the database. Prefix-Projection filtering algorithm enforces domain consistency on the variable succeeding the current frequent prefix in polynomial time. This global constraint also allows for a straightforward implementation of additional constraints such as size, item membership, regular expressions and any combination of them. Experimental results show that our approach clearly outperforms existing CP approaches and competes well with the state-of-the-art methods on large datasets for mining frequent sequential patterns, sequential patterns under various constraints, and top-k sequential patterns. Unlike existing CP methods, our approach achieves a better scalability.     

Optimizing top-<Emphasis Type="Italic">k</Emphasis> retrieval: submodularity analysis and search strategies

The key issue in top-k retrieval, finding a set of k documents (from a large document collection) that can best answer a user’s query, is to strike the optimal balance between relevance and diversity. In this paper, we study the top-k retrieval problem in the framework of facility location analysis and prove the submodularity of that objective function which provides a theoretical approximation guarantee of factor 1?\(\frac{1}{e}\) for the (best-first) greedy search algorithm. Furthermore, we propose a two-stage hybrid search strategy which first obtains a high-quality initial set of top-k documents via greedy search, and then refines that result set iteratively via local search. Experiments on two large TREC benchmark datasets show that our two-stage hybrid search strategy approach can supersede the existing ones effectively and efficiently.     

Time-weighted counting for recently frequent pattern mining in data streams

How can we discover interesting patterns from time-evolving high-speed data streams? How to analyze the data streams quickly and accurately, with little space overhead? How to guarantee the found patterns to be self-consistent? High-speed data stream has been receiving increasing attention due to its wide applications such as sensors, network traffic, social networks, etc. The most fundamental task on the data stream is frequent pattern mining; especially, focusing on recentness is important in real applications. In this paper, we develop two algorithms for discovering recently frequent patterns in data streams. First, we propose TwMinSwap to find top-k recently frequent items in data streams, which is a deterministic version of our motivating algorithm TwSample providing theoretical guarantees based on item sampling. TwMinSwap improves TwSample in terms of speed, accuracy, and memory usage. Both require only O(k) memory spaces and do not require any prior knowledge on the stream such as its length and the number of distinct items in the stream. Second, we propose TwMinSwap-Is to find top-k recently frequent itemsets in data streams. We especially focus on keeping self-consistency of the discovered itemsets, which is the most important property for reliable results, while using O(k) memory space with the assumption of a constant itemset size. Through extensive experiments, we demonstrate that TwMinSwap outperforms all competitors in terms of accuracy and memory usage, with fast running time. We also show that TwMinSwap-Is is more accurate than the competitor and discovers recently frequent itemsets with reasonably large sizes (at most 5–7) depending on datasets. Thanks to TwMinSwap and TwMinSwap-Is, we report interesting discoveries in real world data streams, including the difference of trends between the winner and the loser of U.S. presidential candidates, and temporal human contact patterns.     

Top-<Emphasis Type="Italic">k</Emphasis> coupled keyword recommendation for relational keyword queries

Providing top-k typical relevant keyword queries would benefit the users who cannot formulate appropriate queries to express their imprecise query intentions. By extracting the semantic relationships both between keywords and keyword queries, this paper proposes a new keyword query suggestion approach which can provide typical and semantically related queries to the given query. Firstly, a keyword coupling relationship measure, which considers both intra- and inter-couplings between each pair of keywords, is proposed. Then, the semantic similarity of different keyword queries can be measured by using a semantic matrix, in which the coupling relationships between keywords in queries are reserved. Based on the query semantic similarities, we next propose an approximation algorithm to find the most typical queries from query history by using the probability density estimation method. Lastly, a threshold-based top-k query selection method is proposed to expeditiously evaluate the top-k typical relevant queries. We demonstrate that our keyword coupling relationship and query semantic similarity measures can capture the coupling relationships between keywords and semantic similarities between keyword queries accurately. The efficiency of query typicality analysis and top-k query selection algorithm is also demonstrated.     

Mining collective knowledge: inferring functional labels from online review for business

Uncertain graph has been widely used to represent graph data with inherent uncertainty in structures. Reliability search is a fundamental problem in uncertain graph analytics. This paper investigates on a new problem with broad real-world applications, the top-k reliability search problem on uncertain graphs, that is, finding the k vertices v with the highest reliabilities of connections from a source vertex s to v. Note that the existing algorithm for the threshold-based reliability search problem is inefficient for the top-k reliability search problem. We propose a new algorithm to efficiently solve the top-k reliability search problem. The algorithm adopts two important techniques, namely the BFS sharing technique and the offline sampling technique. The BFS sharing technique exploits overlaps among different sampled possible worlds of the input uncertain graph and performs a single BFS on all possible worlds simultaneously. The offline sampling technique samples possible worlds offline and stores them using a compact structure. The algorithm also takes advantages of bit vectors and bitwise operations to improve efficiency. In addition, we generalize the top-k reliability search problem from single-source case to the multi-source case and show that the multi-source case of the problem can be equivalently converted to the single-source case of the problem. Moreover, we define two types of the reverse top-k reliability search problems with different semantics on uncertain graphs. We propose appropriate solutions for both of them. Extensive experiments carried out on both real and synthetic datasets verify that the optimized algorithm outperforms the baselines by 1–2 orders of magnitude in execution time while achieving comparable accuracy. Meanwhile, the optimized algorithm exhibits linear scalability with respect to the size of the input uncertain graph.     

Adaptive query relaxation and top-<Emphasis Type="Italic">k</Emphasis> result ranking over autonomous web databases

Internet users may suffer the empty or too little answer problem when they post a strict query to the Web database. To address this problem, we develop a general framework to enable automatically query relaxation and top-k result ranking. Our framework consists of two processing steps. The first step is query relaxation. Based on the user original query, we speculate how much the user cares about each specified attribute by measuring its specified value distribution in the database. The rare distribution of the specified value of the attribute indicates the attribute may important for the user. According to the attribute importance, the original query is then rewritten as a relaxed query by expanding each query criterion range. The relaxed degree on each specified attribute is varied with the attribute weight adaptively. The most important attribute is relaxed with the minimum degree so that the answer returned by the relaxed query can be most relevant to the user original intention. The second step is top-k result ranking. In this step, we first generate user contextual preferences from query history and then use them to create a priori orders of tuples during the off-line pre-processing. Only a few representative orders are saved, each corresponding to a set of contexts. Then, these orders and associated contexts are used at querying time to expeditiously provide top-k relevant answers by using the top-k evaluation algorithm. Results of a preliminary user study demonstrate our query relaxation, and top-k result ranking methods can capture the users preferences effectively. The efficiency and effectiveness of our approach is also demonstrated.     

Parallel <Emphasis Type="Italic">LL</Emphasis> parsing

A deterministic parallel LL parsing algorithm is presented. The algorithm is based on a transformation from a parsing problem to parallel reduction. First, a nondeterministic version of a parallel LL parser is introduced. Then, it is transformed into the deterministic version—the LLP parser. The deterministic LLP(q,k) parser uses two kinds of information to select the next operation — a lookahead string of length up to k symbols and a lookback string of length up to q symbols. Deterministic parsing is available for LLP grammars, a subclass of LL grammars. Since the presented deterministic and nondeterministic parallel parsers are both based on parallel reduction, they are suitable for most parallel architectures.     

An effective suggestion method for keyword search of databases

This paper solves the problem of providing high-quality suggestions for user keyword queries over databases. With the assumption that the returned suggestions are independent, existing query suggestion methods over databases score candidate suggestions individually and return the top-k best of them. However, the top-k suggestions have high redundancy with respect to the topics. To provide informative suggestions, the returned k suggestions are expected to be diverse, i.e., maximizing the relevance to the user query and the diversity with respect to topics that the user might be interested in simultaneously. In this paper, an objective function considering both factors is defined for evaluating a suggestion set. We show that maximizing the objective function is a submodular function maximization problem subject to n matroid constraints, which is an NP-hard problem. An greedy approximate algorithm with an approximation ratio O(\(\frac {1}{1+n}\)) is also proposed. Experimental results show that our suggestion outperforms other methods on providing relevant and diverse suggestions.     

On the <Emphasis Type="Italic">k</Emphasis>-accessibility of cores of <Emphasis Type="Italic">TU</Emphasis>-cooperative games

This paper proposes a strengthening of the author’s core-accessibility theorem for balanced TU-cooperative games. The obtained strengthening relaxes the influence of the nontransitivity of classical domination αv on the quality of the sequential improvement of dominated imputations in a game v. More specifically, we establish the k-accessibility of the core C(α _v ) of any balanced TU-cooperative game v for all natural numbers k: for each dominated imputation x, there exists a converging sequence of imputations x₀, x₁,..., such that x₀ = x, lim x _r ∈ C(α _v ) and x_r?m is dominated by any successive imputation x _r with m ∈ [1, k] and r ≥ m. For showing that the TU-property is essential to provide the k-accessibility of the core, we give an example of an NTU-cooperative game G with a ”black hole” representing a nonempty closed subset B ? G(N) of dominated imputations that contains all the α _G -monotonic sequential improvement trajectories originating at any point x ∈ B.     

A cellular automaton for blocking queen games

We show that the winning positions of a certain type of two-player game form interesting patterns which often defy analysis, yet can be computed by a cellular automaton. The game, known as Blocking Wythoff Nim, consists of moving a queen as in chess, but always towards (0, 0), and it may not be moved to any of \(k-1\) temporarily “blocked” positions specified on the previous turn by the other player. The game ends when a player wins by blocking all possible moves of the other player. The value of k is a parameter that defines the game, and the pattern of winning positions can be very sensitive to k. As k becomes large, parts of the pattern of winning positions converge to recurring chaotic patterns that are independent of k. The patterns for large k display an unprecedented amount of self-organization at many scales, and here we attempt to describe the self-organized structure that appears. This paper extends a previous study (Cook et al. in Cellular automata and discrete complex systems, AUTOMATA 2015, Lecture Notes in Computer Science, vol 9099, pp 71–84, 2015), containing further analysis and new insights into the long term behaviour and structures generated by our blocking queen cellular automaton.     

The Number of Tree Stars Is <Emphasis Type="Italic">O</Emphasis><Superscript>*</Superscript>(1.357<Superscript><Emphasis Type="Italic">k</Emphasis></Superscript>)

Every rectilinear Steiner tree problem admits an optimal tree T ^* which is composed of tree stars. Moreover, the currently fastest algorithms for the rectilinear Steiner tree problem proceed by composing an optimum tree T ^* from tree star components in the cheapest way. The efficiency of such algorithms depends heavily on the number of tree stars (candidate components). Fößmeier and Kaufmann (Algorithmica 26, 68–99, 2000) showed that any problem instance with k terminals has a number of tree stars in between 1.32 ^k and 1.38 ^k (modulo polynomial factors) in the worst case. We determine the exact bound O ^*(ρ ^k ) where ρ≈1.357 and mention some consequences of this result.     

<Emphasis Type="Italic">k</Emphasis>-most suitable locations selection

Choosing the best location for starting a business or expanding an existing enterprize is an important issue. A number of location selection problems have been discussed in the literature. They often apply the Reverse Nearest Neighbor as the criterion for finding suitable locations. In this paper, we apply the Average Distance as the criterion and propose the so-called k-most suitable locations (k-MSL) selection problem. Given a positive integer k and three datasets: a set of customers, a set of existing facilities, and a set of potential locations. The k-MSL selection problem outputs k locations from the potential location set, such that the average distance between a customer and his nearest facility is minimized. In this paper, we formally define the k-MSL selection problem and show that it is NP-hard. We first propose a greedy algorithm which can quickly find an approximate result for users. Two exact algorithms are then proposed to find the optimal result. Several pruning rules are applied to increase computational efficiency. We evaluate the algorithms’ performance using both synthetic and real datasets. The results show that our algorithms are able to deal with the k-MSL selection problem efficiently.