<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.     

(1+4)-dimensional spherically symmetric black holes in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>)

New non-vacuum spherically symmetric solutions in (1+4)-dimensional space-time are derived using the field equations of f(T) theory, where T is the torsion scalar defined as \(T\mathop = \limits^{def} {T^\mu }_{\nu \rho }S_\mu ^{\nu \rho }\). The energy density, radial and transversal pressures in these solutions are shown to satisfy the energy conditions. Other interesting solutions are obtained under the constraint of vanishing radial pressure for different choices of f(T). Impositions are provided to reproduce the (1+4)-dimensional AdS-Schwarzschild solution. In the quadratic case, i.e., f(T) ∝ T ², other impositions are derived and have shown to satisfy the non-diagonal components of the field equations of f(T) theory. The physics relevant to the resulting models is discussed.     

The direction-constrained <Emphasis Type="Italic">k</Emphasis> nearest neighbor query

Finding k nearest neighbor objects in spatial databases is a fundamental problem in many geospatial systems and the direction is one of the key features of a spatial object. Moreover, the recent tremendous growth of sensor technologies in mobile devices produces an enormous amount of spatio-directional (i.e., spatially and directionally encoded) objects such as photos. Therefore, an efficient and proper utilization of the direction feature is a new challenge. Inspired by this issue and the traditional k nearest neighbor search problem, we devise a new type of query, called the direction-constrained k nearest neighbor (DCkNN) query. The DCkNN query finds k nearest neighbors from the location of the query such that the direction of each neighbor is in a certain range from the direction of the query. We develop a new index structure called MULTI, to efficiently answer the DCkNN query with two novel index access algorithms based on the cost analysis. Furthermore, our problem and solution can be generalized to deal with spatio-circulant dimensional (such as a direction and circulant periods of time such as an hour, a day, and a week) objects. Experimental results show that our proposed index structure and access algorithms outperform two adapted algorithms from existing kNN algorithms.     

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.     

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.     

Multiple <Emphasis Type="Italic">k</Emphasis> nearest neighbor search

The problem of kNN (k Nearest Neighbor) queries has received considerable attention in the database and information retrieval communities. Given a dataset D and a kNN query q, the k nearest neighbor algorithm finds the closest k data points to q. The applications of kNN queries are board, not only in spatio-temporal databases but also in many areas. For example, they can be used in multimedia databases, data mining, scientific databases and video retrieval. The past studies of kNN query processing did not consider the case that the server may receive multiple kNN queries at one time. Their algorithms process queries independently. Thus, the server will be busy with continuously reaccessing the database to obtain the data that have already been acquired. This results in wasting I/O costs and degrading the performance of the whole system. In this paper, we focus on this problem and propose an algorithm named COrrelated kNN query Evaluation (COKE). The main idea of COKE is an “information sharing” strategy whereby the server reuses the query results of previously executed queries for efficiently processing subsequent queries. We conduct a comprehensive set of experiments to analyze the performance of COKE and compare it with the Best-First Search (BFS) algorithm. Empirical studies indicate that COKE outperforms BFS, and achieves lower I/O costs and less running time.     

On <Emphasis Type="Italic">m</Emphasis>-Near-Resolvable Block Designs and <Emphasis Type="Italic">q</Emphasis>-ary Constant-Weight Codes

We introduce m-near-resolvable block designs. We establish a correspondence between such block designs and a subclass of (optimal equidistant) q-ary constant-weight codes meeting the Johnson bound. We present constructions of m-near-resolvable block designs, in particular based on Steiner systems and super-simple t-designs.     

Pseudo-Randomness of Certain Sequences of <Emphasis Type="Italic">k</Emphasis> Symbols with Length <Emphasis Type="Italic">pq</Emphasis>

The theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sárközy and later extended to sequences of k symbols (or k-ary sequences). Certain constructions of pseudo-random sequences of k symbols were presented over finite fields in the literature. In this paper, two families of sequences of k symbols are constructed by using the integers modulo pq for distinct odd primes p and q. The upper bounds on the well-distribution measure and the correlation measure of the families sequences are presented in terms of certain character sums over modulo pq residue class rings. And low bounds on the linear complexity profile are also estimated.     

Transit cosmological models with domain walls in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R,T</Emphasis>) gravity

We study the physical behavior of the transition of a 5D perfect fluid universe from an early decelerating phase to the current accelerating phase in the framework of f(R, T) theory of gravity in the presence of domain walls. The fifth dimension is not observed because it is compact. To determine the solution of the field equations, we use the concept of a time-dependent deceleration parameter which yields the scale factor a(t) = sinh^1/n(αt), where n and α are positive constants. For 0 < n ≤ 1, this generates a class of accelerating models, while for n > 1 the universe attains a phase transition from an early decelerating phase to the present accelerating phase, consistent with the recent observations. Some physical and geometric properties of the models are also discussed.     

On transitive partitions of an <Emphasis Type="Italic">n</Emphasis>-cube into codes

We present methods to construct transitive partitions of the set E ⁿ of all binary vectors of length n into codes. In particular, we show that for all n = 2 ^k ? 1, k ≥ 3, there exist transitive partitions of E ⁿ into perfect transitive codes of length n.     

The <Emphasis Type="Italic">B</Emphasis><Superscript><Emphasis Type="Italic">dual</Emphasis></Superscript>-Tree: indexing moving objects by space filling curves in the dual space

Existing spatiotemporal indexes suffer from either large update cost or poor query performance, except for the B ^x -tree (the state-of-the-art), which consists of multiple B ⁺-trees indexing the 1D values transformed from the (multi-dimensional) moving objects based on a space filling curve (Hilbert, in particular). This curve, however, does not consider object velocities, and as a result, query processing with a B ^x -tree retrieves a large number of false hits, which seriously compromises its efficiency. It is natural to wonder “can we obtain better performance by capturing also the velocity information, using a Hilbert curve of a higher dimensionality?”. This paper provides a positive answer by developing the B ^dual -tree, a novel spatiotemporal access method leveraging pure relational methodology. We show, with theoretical evidence, that the B ^dual -tree indeed outperforms the B ^x -tree in most circum- stances. Furthermore, our technique can effectively answer progressive spatiotemporal queries, which are poorly supported by B ^x -trees.     

Participant selection for <Emphasis Type="Italic">t</Emphasis>-sweep <Emphasis Type="Italic">k</Emphasis>-coverage crowd sensing tasks

With the popularization of wireless networks and mobile intelligent terminals, mobile crowd sensing is becoming a promising sensing paradigm. Tasks are assigned to users with mobile devices, which then collect and submit ambient information to the server. The composition of participants greatly determines the quality and cost of the collected information. This paper aims to select fewest participants to achieve the quality required by a sensing task. The requirement namely “t-sweep k-coverage” means for a target location, every t time interval should at least k participants sense. The participant selection problem for “t-sweep k-coverage” crowd sensing tasks is NP-hard. Through delicate matrix stacking, linear programming can be adopted to solve the problem when it is in small size. We further propose a participant selection method based on greedy strategy. The two methods are evaluated through simulated experiments using users’ call detail records. The results show that for small problems, both the two methods can find a participant set meeting the requirement. The number of participants picked by the greedy based method is roughly twice of the linear programming based method. However, when problems become larger, the linear programming based method performs unstably, while the greedy based method can still output a reasonable solution.     

Incremental <Emphasis Type="Italic">k</Emphasis>-core decomposition: algorithms and evaluation

A k-core of a graph is a maximal connected subgraph in which every vertex is connected to at least k vertices in the subgraph. k-core decomposition is often used in large-scale network analysis, such as community detection, protein function prediction, visualization, and solving NP-hard problems on real networks efficiently, like maximal clique finding. In many real-world applications, networks change over time. As a result, it is essential to develop efficient incremental algorithms for dynamic graph data. In this paper, we propose a suite of incremental k-core decomposition algorithms for dynamic graph data. These algorithms locate a small subgraph that is guaranteed to contain the list of vertices whose maximum k-core values have changed and efficiently process this subgraph to update the k-core decomposition. We present incremental algorithms for both insertion and deletion operations, and propose auxiliary vertex state maintenance techniques that can further accelerate these operations. Our results show a significant reduction in runtime compared to non-incremental alternatives. We illustrate the efficiency of our algorithms on different types of real and synthetic graphs, at varying scales. For a graph of 16 million vertices, we observe relative throughputs reaching a million times, relative to the non-incremental algorithms.     

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.     

(<Emphasis Type="Italic">a</Emphasis>, <Emphasis Type="Italic">d</Emphasis>)-Distance Antimagic Labeling of Some Types of Graphs

We analyze the necessary existence conditions for (a, d)-distance antimagic labeling of a graph G = (V, E) of order n. We obtain theorems that expand the family of not (a, d) -distance antimagic graphs. In particular, we prove that the crown P _n ○ P ₁ does not admit an (a, 1)-distance antimagic labeling for n ≥ 2 if a ≥ 2. We determine the values of a at which path P _n can be an (a, 1)-distance antimagic graph. Among regular graphs, we investigate the case of a circulant graph.     

Some results on the minimal coverings of precomplete classes in partial<Emphasis Type="Italic">k</Emphasis>-valued logic functions

In completeness theories of multiple-valued logic, the characterization of Sheffer functions is an important issue. The solution can be reduced to determining the minimal coverings of precomplete classes. In this paper, someFull Symmetric Function Sets (m=3) are proved to be components of the minimal covering of precomplete classes inP _k ^* .     

On partitions of an <Emphasis Type="Italic">n</Emphasis>-cube into nonequivalent perfect codes

We prove that for all n = 2^k ? 1, k ≥ 5, there exists a partition of the set of all binary vectors of length n into pairwise nonequivalent perfect binary codes of length n with distance 3.     

Testing list <Emphasis Type="Italic">H</Emphasis>-homomorphisms

In the List H- Homomorphism Problem, for a graph H that is a parameter of the problem, an instance consists of an undirected graph G with a list constraint \({L(v) \subseteq V(H)}\) for each variable \({v \in V(G)}\), and the objective is to determine whether there is a list H-homomorphism \({f:V(G) \to V(H)}\), that is, \({f(v) \in L(v)}\) for every \({v \in V(G)}\) and \({(f(u),f(v)) \in E(H)}\) whenever \({(u,v) \in E(G)}\).We consider the problem of testing list H-homomorphisms in the following weighted setting: An instance consists of an undirected graph G, list constraints L, weights imposed on the vertices of G, and a map \({f:V(G) \to V(H)}\) given as an oracle access. The objective is to determine whether f is a list H-homomorphism or far from any list H-homomorphism. The farness is measured by the total weight of vertices \({v \in V(G)}\) for which f(v) must be changed so as to make f a list H-homomorphism. In this paper, we classify graphs H with respect to the number of queries to f required to test the list H-homomorphisms. Specifically, we show that (i) list H-homomorphisms are testable with a constant number of queries if and only if H is a reflexive complete graph or an irreflexive complete bipartite graph and (ii) list H-homomorphisms are testable with a sublinear number of queries if and only if H is a bi-arc graph.     

Efficient <Emphasis Type="Italic">l</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript> norm based sparse subspace clustering via smooth IRLS and ADMM

Recently, sparse subspace clustering, as a subspace learning technique, has been successfully applied to several computer vision applications, e.g. face clustering and motion segmentation. The main idea of sparse subspace clustering is to learn an effective sparse representation that are used to construct an affinity matrix for spectral clustering. While most of existing sparse subspace clustering algorithms and its extensions seek the forms of convex relaxation, the use of non-convex and non-smooth l _q (0 < q < 1) norm has demonstrated better recovery performance. In this paper we propose an l _q norm based Sparse Subspace Clustering method (lqSSC), which is motivated by the recent work that l _q norm can enhance the sparsity and make better approximation to l ₀ than l ₁. However, the optimization of l _q norm with multiple constraints is much difficult. To solve this non-convex problem, we make use of the Alternating Direction Method of Multipliers (ADMM) for solving the l _q norm optimization, updating the variables in an alternating minimization way. ADMM splits the unconstrained optimization into multiple terms, such that the l _q norm term can be solved via Smooth Iterative Reweighted Least Square (SIRLS), which converges with guarantee. Different from traditional IRLS algorithms, the proposed algorithm is based on gradient descent with adaptive weight, making it well suit for general sparse subspace clustering problem. Experiments on computer vision tasks (synthetic data, face clustering and motion segmentation) demonstrate that the proposed approach achieves considerable improvement of clustering accuracy than the convex based subspace clustering methods.     

Know your customer: computing <Emphasis Type="Italic">k</Emphasis>-most promising products for targeted marketing

The advancement of World Wide Web has revolutionized the way the manufacturers can do business. The manufacturers can collect customer preferences for products and product features from their sales and other product-related Web sites to enter and sustain in the global market. For example, the manufactures can make intelligent use of these customer preference data to decide on which products should be selected for targeted marketing. However, the selected products must attract as many customers as possible to increase the possibility of selling more than their respective competitors. This paper addresses this kind of product selection problem. That is, given a database of existing products P from the competitors, a set of company’s own products Q, a dataset C of customer preferences and a positive integer k, we want to find k-most promising products (k-MPP) from Q with maximum expected number of total customers for targeted marketing. We model k-MPP query and propose an algorithmic framework for processing such query and its variants. Our framework utilizes grid-based data partitioning scheme and parallel computing techniques to realize k-MPP query. The effectiveness and efficiency of the framework are demonstrated by conducting extensive experiments with real and synthetic datasets.