Testing Convexity Properties of Tree Colorings

A coloring of a graph is convex if it induces a partition of the vertices into connected subgraphs. Besides being an interesting property from a theoretical point of view, tests for convexity have applications in various areas involving large graphs. We study the important subcase of testing for convexity in trees. This problem is linked, among other possible applications, with the study of phylogenetic trees, which are central in genetic research, and are used in linguistics and other areas. We give a 1-sided, non-adaptive, distribution-free ε-test for the convexity of tree colorings. The query complexity of our test is O(k/ε), where k is the number of colors, and the additional computational complexity is O(n). On the other hand, we prove a lower bound of \(\Omega(\sqrt{k/\epsilon})\) on the query complexity of tests for convexity in the standard model, which applies even for (unweighted) paths. We also consider whether the dependency on k can be reduced in some cases, and provide an alternative testing algorithm for the case of paths. Then we investigate a variant of convexity, namely quasi-convexity, in which all but one of the colors are required to induce connected components. For this problem we provide a 1-sided, non-adaptive ε-test with query complexity O(k/ε ²) and time complexity O(kn/ε). For both our convexity and quasi-convexity tests, we show that, assuming that a query takes constant time, the time complexity can be reduced to a constant independent of n if we allow a preprocessing stage of time O(n) and O(n ²), respectively. Finally, we show how to test for a variation of convexity and quasi-convexity where the maximum number of connectivity classes of each color is allowed to be a constant value other than 1.     

Reverse Furthest Neighbors Query in Road Networks

Given a road network G = (V,E), where V (E) denotes the set of vertices(edges) in G, a set of points of interest P and a query point q residing in G, the reverse furthest neighbors (Rfn _R ) query in road networks fetches a set of points p ∈ P that take q as their furthest neighbor compared with all points in P ∪ {q}. This is the monochromatic Rfn _R (Mrfn _R ) query. Another interesting version of Rfn _R query is the bichromatic reverse furthest neighbor (Brfn _R ) query. Given two sets of points P and Q, and a query point q ∈ Q, a Brfn _R query fetches a set of points p ∈ P that take q as their furthest neighbor compared with all points in Q. This paper presents efficient algorithms for both Mrfn _R and Brfn _R queries, which utilize landmarks and partitioning-based techniques. Experiments on real datasets confirm the efficiency and scalability of proposed algorithms.     

Property-Preserving Data Reconstruction

We initiate a new line of investigation into online property-preserving data reconstruction. Consider a dataset which is assumed to satisfy various (known) structural properties; e.g., it may consist of sorted numbers, or points on a manifold, or vectors in a polyhedral cone, or codewords from an error-correcting code. Because of noise and errors, however, an (unknown) fraction of the data is deemed unsound, i.e., in violation with the expected structural properties. Can one still query into the dataset in an online fashion and be provided data that is always sound? In other words, can one design a filter which, when given a query to any item I in the dataset, returns a sound item J that, although not necessarily in the dataset, differs from I as infrequently as possible. No preprocessing should be allowed and queries should be answered online.We consider the case of a monotone function. Specifically, the dataset encodes a function f:{1,…,n}?? R that is at (unknown) distance ε from monotone, meaning that f can—and must—be modified at ε n places to become monotone.Our main result is a randomized filter that can answer any query in O(log?² nlog? log?n) time while modifying the function f at only O(ε n) places. The amortized time over n function evaluations is O(log?n). The filter works as stated with probability arbitrarily close to 1. We provide an alternative filter with O(log?n) worst case query time and O(ε nlog?n) function modifications. For reconstructing d-dimensional monotone functions of the form f:{1,…,n} ^d ? ? R, we present a filter that takes (2 ^O(d)(log?n)^4d?2log?log?n) time per query and modifies at most O(ε n ^d ) function values (for constant d).     

Bionic knowledge and information reuse methodology for uncertainty minimization in product design

Given two spatial point sets R and B in the plane, with cardinalities m and n, respectively, and stored in two separate R-trees, we propose an efficient algorithm to verify whether R and B are linearly separable. The sets R and B are linearly separable if there exists a line that splits the plane into to halfplanes, one containing all R and the other one containing all B. This is the first algorithm that answers the separability question in the context of the spatial data bases. That is, it considers as input big spatial data stored in secondary storage data structures (e.g., the R-tree) which are not allowed to be completely stored in the main memory of the computer to run a classic algorithm. The algorithms designed in this context aim to minimize as much as possible the number of blocks read from the secondary storage data structures to the main memory. Studied problems in this setting are the k-nearest neighbor problem and the spatial range query problem. Our algorithm explicitly exploits the geometric and spatial properties of the R-trees to access only the nodes relevant to decide the linear separability of the given sets. Our experimental results show the efficiency of the algorithm, since it accesses between the 0.34 and 2.79% of the nodes of the R-trees. We also analyze the asymptotic running time of the algorithm, showing that it runs in \(O(m\log m + n\log n)\) time in the worst case.     

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.     

On Fixed Cost k-Flow Problems

In the Fixed Cost k-Flow problem, we are given a graph G = (V, E) with edge-capacities {u _e ∣e ∈ E} and edge-costs {c _e ∣e ∈ E}, source-sink pair s, t ∈ V, and an integer k. The goal is to find a minimum cost subgraph H of G such that the minimum capacity of an st-cut in H is at least k. By an approximation-preserving reduction from Group Steiner Tree problem to Fixed Cost k-Flow, we obtain the first polylogarithmic lower bound for the problem; this also implies the first non-constant lower bounds for the Capacitated Steiner Network and Capacitated Multicommodity Flow problems. We then consider two special cases of Fixed Cost k-Flow. In the Bipartite Fixed-Cost k-Flow problem, we are given a bipartite graph G = (A ∪ B, E) and an integer k > 0. The goal is to find a node subset S ? A ∪ B of minimum size |S| such G has k pairwise edge-disjoint paths between S ∩ A and S ∩ B. We give an \(O(\sqrt {k\log k})\) approximation for this problem. We also show that we can compute a solution of optimum size with Ω(k/polylog(n)) paths, where n = |A| + |B|. In the Generalized-P2P problem we are given an undirected graph G = (V, E) with edge-costs and integer charges {b _v : v ∈ V}. The goal is to find a minimum-cost spanning subgraph H of G such that every connected component of H has non-negative charge. This problem originated in a practical project for shift design [11]. Besides that, it generalizes many problems such as Steiner Forest, k-Steiner Tree, and Point to Point Connection. We give a logarithmic approximation algorithm for this problem. Finally, we consider a related problem called Connected Rent or Buy Multicommodity Flow and give a log^3+?? n approximation scheme for it using Group Steiner Tree techniques.     

On Detection of Gaussian Stochastic Sequences

We consider the minimax detection problem for a Gaussian random signal vector in white Gaussian additive noise. It is assumed that an unknown vector σ of signal vector intensities belongs to a given set ε. We investigate when it is possible to replace the set ε with a smaller set ε₀ without loss of quality (and, in particular, replace it with a single point σ₀).     

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.     

Continuous visible nearest neighbor query processing in spatial databases

In this paper, we identify and solve a new type of spatial queries, called continuous visible nearest neighbor (CVNN) search. Given a data set P, an obstacle set O, and a query line segment q in a two-dimensional space, a CVNN query returns a set of \({\langle p, R\rangle}\) tuples such that \({p \in P}\) is the nearest neighbor to every point r along the interval \({R \subseteq q}\) as well as p is visible to r. Note that p may be NULL, meaning that all points in P are invisible to all points in R due to the obstruction of some obstacles in O. In contrast to existing continuous nearest neighbor query, CVNN retrieval considers the impact of obstacles on visibility between objects, which is ignored by most of spatial queries. We formulate the problem, analyze its unique characteristics, and develop efficient algorithms for exact CVNN query processing. Our methods (1) utilize conventional data-partitioning indices (e.g., R-trees) on both P and O, (2) tackle the CVNN search by performing a single query for the entire query line segment, and (3) only access the data points and obstacles relevant to the final query result by employing a suite of effective pruning heuristics. In addition, several interesting variations of CVNN queries have been introduced, and they can be supported by our techniques, which further demonstrates the flexibility of the proposed algorithms. A comprehensive experimental evaluation using both real and synthetic data sets has been conducted to verify the effectiveness of our proposed pruning heuristics and the performance of our proposed algorithms.     

Negativity in the generalized Valence Bond Solid state

Using a graphical presentation of the spin S one-dimensional Valence Bond Solid (VBS) state, based on the representation theory of the \({\textit{SU}}(2)\) Lie algebra of spins, we compute the spectrum of a mixed-state reduced density matrix. This mixed state of two blocks of spins A and B is obtained by tracing out the spins outside A and B, in the pure VBS state density matrix. We find in particular that the negativity of the mixed state is nonzero only for adjacent subsystems. The method introduced here can be generalized to the computation of entanglement properties in Levin–Wen models, that possess a similar algebraic structure to the VBS state in the ground state.     

Tractable queries on big data via preprocessing with logarithmic-size output

Given a set S of points in the two-dimensional space, which are stored in a spatial database, this paper presents an efficient algorithm to find, in the area delimited by those points, the empty circle with the largest area that contains only a query point q. Our algorithm adapts previous work in the field of computational geometry to be used in spatial databases, which requires to manage large amounts of data. To achieve this objective, the basic idea is to discard a large part of the points of S, in such a way that the problem can be solved providing only the remaining points to a classical computational geometry algorithm that, by processing a smaller collection of points, saves main memory resources and computation time. The correctness of our algorithm is formally proven. In addition, we empirically show its efficiency and scalability by running a set of experiments using both synthetic and real data.     

Making Doubling Metrics Geodesic

The starting point of our research is the following problem: given a doubling metric ?=(V,d), can one (efficiently) find an unweighted graph G′=(V′,E′) with V?V′ whose shortest-path metric d′ is still doubling, and which agrees with d on V×V? While it is simple to show that the answer to the above question is negative if distances must be preserved exactly. However, allowing a (1+ε) distortion between d and d′ enables us bypass this hurdle, and obtain an unweighted graph G′ with doubling dimension at most a factor O(log?ε ^?1) times the doubling dimension of G.More generally, this paper gives algorithms that construct graphs G′ whose convex (or geodesic) closure has doubling dimension close to that of ?, and the shortest-path distances in G′ closely approximate those of ? when restricted to V×V. Similar results are shown when the metric ? is an additive (tree) metric and the graph G′ is restricted to be a tree.     

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.     

Efficient moving <Emphasis Type="Italic">k</Emphasis> nearest neighbor queries over line segment objects

The growing need for location based services motivates the moving k nearest neighbor query (MkNN), which requires to find the k nearest neighbors of a moving query point continuously. In most existing solutions, data objects are abstracted as points. However, lots of real-world data objects, such as roads, rivers or pipelines, should be reasonably modeled as line segments or polyline segments. In this paper, we present LV*-Diagram to handle MkNN queries over line segment data objects. LV*-Diagram dynamically constructs a safe region. The query results remain unchanged if the query point is in the safe region, and hence, the computation cost of the server is greatly reduced. Experimental results show that our approach significantly outperforms the baseline method w.r.t. CPU load, I/O, and communication costs.     

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.     

New plane-sweep algorithms for distance-based join queries in spatial databases

Efficient and effective processing of the distance-based join query (DJQ) is of great importance in spatial databases due to the wide area of applications that may address such queries (mapping, urban planning, transportation planning, resource management, etc.). The most representative and studied DJQs are the K Closest Pairs Query (KCPQ) and εDistance Join Query (εDJQ). These spatial queries involve two spatial data sets and a distance function to measure the degree of closeness, along with a given number of pairs in the final result (K) or a distance threshold (ε). In this paper, we propose four new plane-sweep-based algorithms for KCPQs and their extensions for εDJQs in the context of spatial databases, without the use of an index for any of the two disk-resident data sets (since, building and using indexes is not always in favor of processing performance). They employ a combination of plane-sweep algorithms and space partitioning techniques to join the data sets. Finally, we present results of an extensive experimental study, that compares the efficiency and effectiveness of the proposed algorithms for KCPQs and εDJQs. This performance study, conducted on medium and big spatial data sets (real and synthetic) validates that the proposed plane-sweep-based algorithms are very promising in terms of both efficient and effective measures, when neither inputs are indexed. Moreover, the best of the new algorithms is experimentally compared to the best algorithm that is based on the R-tree (a widely accepted access method), for KCPQs and εDJQs, using the same data sets. This comparison shows that the new algorithms outperform R-tree based algorithms, in most cases.     

Answering subgraph queries over massive disk resident graphs

Due to its wide applications, subgraph query has attracted lots of attentions in database community. In this paper, we focus on subgraph query over a single large graph G, i.e., finding all embeddings of query Q in G. Different from existing feature-based approaches, we map all edges into a two-dimensional space R ² and propose a bitmap structure to index R ². At run time, we find a set of adjacent edge pairs (AEP) or star-style patterns (SSP) to cover Q. We develop edge join (EJ) algorithms to address both AEP and SSP subqueries. Based on the bitmap index, our method can optimize I/O and CPU cost. More importantly, our index has the linear space complexity instead of exponential complexity in feature-based approaches, which indicates that our index can scale well with respect to large data size. Furthermore, our index has light maintenance overhead, which has not been considered in most of existing work. Extensive experiments show that our method significantly outperforms existing ones in both online and offline processing with respect to query response time, index building time, index size and index maintenance overhead.     

Resource allocation in cooperative cognitive radio networks towards secure communications for maritime big data systems

In this paper, an innovative framework labeled as cooperative cognitive maritime big data systems (CCMBDSs) on the sea is developed to provide opportunistic channel access and secure communication. A two-phase frame structure is applied to let Secondary users (SUs) entirely utilize the transmission opportunities for a portion of time as the reward by cooperation with Primary users (PUs). Amplify-and-forward (AF) relaying mode is exploited in SU nodes, and Backward induction method based Stackelberg game is employed to achieve optimal determination of SU, power consumption and time portion of cooperation both for non-secure communication scenario and secure communication. Specifically, a jammer-based secure communications scheme is developed to maximize the secure utility of PU, to confront of the situation that the eavesdropper could overheard the signals from SU _i and the jammer. Close-form solutions for the best access time portion as well as the power for SU _i and jammer are derived to realize the Nash Equilibrium. Simulation results validate the effectiveness of our proposed strategy.     

Efficient group-by reverse skyline computation

The reverse skyline query is very useful in many decision making applications. Given a multi-dimensional dataset P and a query point q, the reverse skyline query returns all the points in P whose dynamic skyline contains q. Although the reverse skyline retrieval has been well-studied in the literature, there is, to the best of our knowledge, no prior work on one of the most intuitive and practical types of reverse skyline queries, namely, group-by reverse skyline (GRS) query, which retrieves the reverse skyline for each group in a specified dataset. We formalize the GRS query including monochromatic and bichromatic versions, and identify its properties, and then propose a set of efficient algorithms for computing the group-by reverse skyline. Extensive experimental evaluation using both real and synthetic datasets demonstrates the performance of our proposed algorithms in terms of effectiveness and efficiency under a variety of experimental settings.