Apostolos N. Papadopoulos

R-Trees: Theory and Applications

Space support in databases poses new challenges in every part of a database management system & the capability of spatial support in the physical layer is considered very important. This has led to the design of spatial access methods to enable the effective & efficient management of spatial objects. R-trees have a simplicity of structure & together with their resemblance to the B-tree, allow developers to incorporate them easily into existing database management systems for the support of spatial query processing. This book provides an extensive survey of the R-tree evolution, studying the applicability of the structure & its variations to efficient query processing, accurate proposed cost models, & implementation issues like concurrency control and parallelism. Written for database researchers, designers & programmers as well as graduate students, this comprehensive monograph will be a welcome addition to the field.

Performance of Nearest Neighbor Queries in R-Trees

Nearest neighbor (NN) queries are posed very frequently in spatial applications. Recently a branch- and-bound algorithm based on R-trees has been developed in order to answer efficiently NN queries. In this paper, we combine techniques that were inherently used for the analysis of range and spatial join queries, in order to derive measures regarding the performance of NN queries. We try to estimate the number of disk accesses introduced due to the processing of an NN query. Lower and upper bounds are defined estimating the performance of NN queries very closely. The theoretical analysis is verified with experimental results, under uniform and non-uniform distributions of queries and data, in the 2-dimensional address space.

Fast Nearest-Neighbor Query Processing in Moving-Object Databases

A desirable feature in spatio-temporal databases is the ability to answer future queries, based on the current data characteristics (reference position and velocity vector). Given a moving query and a set of moving objects, a future query asks for the set of objects that satisfy the query in a given time interval. The difficulty in such a case is that both the query and the data objects change positions continuously, and therefore we can not rely on a given fixed reference position to determine the answer. Existing techniques are either based on sampling, or on repetitive application of time-parameterized queries in order to provide the answer. In this paper we develop an efficient method in order to process nearest-neighbor queries in moving-object databases. The basic advantage of the proposed approach is that only one query is issued per time interval. The time-parameterized R-tree structure is used to index the moving objects. An extensive performance evaluation, based on CPU and I/O time, shows that significant improvements are achieved compared to existing techniques.

Structure-based similarity search with graph histograms

Objects like road networks, CAD/CAM components, electrical or electronic circuits, molecules, can be represented as graphs, in many modern applications. The authors propose an efficient and effective graph manipulation technique that can be used in graph-based similarity search. Given a query graph G/sub q/ (V,E), they would like to determine fast which are the graphs in the database that are similar to G/sub q/ (V,E), with respect to a similarity measure. First, they study the similarity measure between two graphs. Then, they discuss graph representation techniques by means of multidimensional vectors. It is shown that no false dismissals are introduced by using the vector representation. Finally they illustrate some representative queries that can be handled by their approach, and present experimental results, based on the proposed graph similarity algorithm. The results show that considerable savings are obtained with respect to computational effort and I/O operations, in comparison to conventional searching techniques.

Continuous monitoring of distance-based outliers over data streams

Anomaly detection is considered an important data mining task, aiming at the discovery of elements (also known as outliers) that show significant diversion from the expected case. More specifically, given a set of objects the problem is to return the suspicious objects that deviate significantly from the typical behavior. As in the case of clustering, the application of different criteria lead to different definitions for an outlier. In this work, we focus on distance-based outliers: an object x is an outlier if there are less than k objects lying at distance at most R from x. The problem offers significant challenges when a stream-based environment is considered, where data arrive continuously and outliers must be detected on-the-fly. There are a few research works studying the problem of continuous outlier detection. However, none of these proposals meets the requirements of modern stream-based applications for the following reasons: (i) they demand a significant storage overhead, (ii) their efficiency is limited and (iii) they lack flexibility. In this work, we propose new algorithms for continuous outlier monitoring in data streams, based on sliding windows. Our techniques are able to reduce the required storage overhead, run faster than previously proposed techniques and offer significant flexibility. Experiments performed on real-life as well as synthetic data sets verify our theoretical study.

Searching for similar trajectories in spatial networks

In several applications, data objects move on pre-defined spatial networks such as road segments, railways, and invisible air routes. Many of these objects exhibit similarity with respect to their traversed paths, and therefore two objects can be correlated based on their motion similarity. Useful information can be retrieved from these correlations and this knowledge can be used to define similarity classes. In this paper, we study similarity search for moving object trajectories in spatial networks. The problem poses some important challenges, since it is quite different from the case where objects are allowed to move freely in any direction without motion restrictions. New similarity measures should be employed to express similarity between two trajectories that do not necessarily share any common sub-path. We define new similarity measures based on spatial and temporal characteristics of trajectories, such that the notion of similarity in space and time is well expressed, and moreover they satisfy the metric properties. In addition, we demonstrate that similarity range queries in trajectories are efficiently supported by utilizing metric-based access methods, such as M-trees.

Nearest-biclusters collaborative filtering based on constant and coherent values

Collaborative Filtering (CF) Systems have been studied extensively for more than a decade to confront the “information overload” problem. Nearest-neighbor CF is based either on similarities between users or between items, to form a neighborhood of users or items, respectively. Recent research has tried to combine the two aforementioned approaches to improve effectiveness. Traditional clustering approaches (k-means or hierarchical clustering) has been also used to speed up the recommendation process. In this paper, we use biclustering to disclose this duality between users and items, by grouping them in both dimensions simultaneously. We propose a novel nearest-biclusters algorithm, which uses a new similarity measure that achieves partial matching of users’ preferences. We apply nearest-biclusters in combination with two different types of biclustering algorithms—Bimax and xMotif—for constant and coherent biclustering, respectively. Extensive performance evaluation results in three real-life data sets are provided, which show that the proposed method improves substantially the performance of the CF process.

A Performance Evaluation of Spatial Join Processing Strategies

We provide an evaluation of query execution plans (QEP) in the case of queries with one or two spatial joins. The QEPs assume R*-tree indexed relations and use a common set of spatial joins algorithms, among which one is a novel extension of a strategy based on an on-the-fly index creation prior to the join with another indexed relation. A common platform is used on which a set of spatial access methods and join algorithms are available. The QEPs are implemented with a general iterator-based spatial query processor, allowing for pipelined QEP execution, thus minimizing memory space required for intermediate results.

SkyGraph: an algorithm for important subgraph discovery in relational graphs

A significant number of applications require effective and efficient manipulation of relational graphs, towards discovering important patterns. Some example applications are: (i) analysis of microarray data in bioinformatics, (ii) pattern discovery in a large graph representing a social network, (iii) analysis of transportation networks, (iv) community discovery in Web data. The basic approach followed by existing methods is to apply mining techniques on graph data to discover important patterns, such as subgraphs that are likely to be useful. However, in some cases the number of mined patterns is large, posing difficulties in selecting the most important ones. For example, applying frequent subgraph mining on a set of graphs the system returns all connected subgraphs whose frequency is above a specified (usually user-defined) threshold. The number of discovered patterns may be large, and this number depends on the data characteristics and the frequency threshold specified. It would be more convenient for the user if “goodness” criteria could be set to evaluate the usefulness of these patterns, and if the user could provide preferences to the system regarding the characteristics of the discovered patterns. In this paper, we propose a methodology to support such preferences by applying subgraph discovery in relational graphs towards retrieving important connected subgraphs. The importance of a subgraph is determined by: (i) the order of the subgraph (the number of vertices) and (ii) the subgraph edge connectivity. The performance of the proposed technique is evaluated by using real-life as well as synthetically generated data sets.

Trajectory Similarity Search in Spatial Networks

In several applications, data objects are assumed to move on predefined spatial networks such as road segments, railways, and invisible air routes. Moving objects may exhibit similarity with respect to their traversed paths, and therefore two objects can be correlated based on their path similarity. In this paper, we study similarity search for moving object trajectories for spatial networks. The problem poses some important challenges, since it is quite different from the case where objects are allowed to move without motion restrictions. Experimental results performed on real-life spatial networks show that trajectory similarity can be supported in an effective and efficient manner by using metric-based access methods