George Kollios

Discovering similar multidimensional trajectories

We investigate techniques for analysis and retrieval of object trajectories in two or three dimensional space. Such data usually contain a large amount of noise, that has made previously used metrics fail. Therefore, we formalize non-metric similarity functions based on the longest common subsequence (LCSS), which are very robust to noise and furthermore provide an intuitive notion of similarity between trajectories by giving more weight to similar portions of the sequences. Stretching of sequences in time is allowed, as well as global translation of the sequences in space. Efficient approximate algorithms that compute these similarity measures are also provided. We compare these new methods to the widely used Euclidean and time warping distance functions (for real and synthetic data) and show the superiority of our approach, especially in the strong presence of noise. We prove a weaker version of the triangle inequality and employ it in an indexing structure to answer nearest neighbor queries. Finally, we present experimental results that validate the accuracy and efficiency of our approach.

Approximate aggregation techniques for sensor databases

In the emerging area of sensor-based systems, a significant challenge is to develop scalable, fault-tolerant methods to extract useful information from the data the sensors collect. An approach to this data management problem is the use of sensor database systems, exemplified by TinyDB and Cougar, which allow users to perform aggregation queries such as MIN, COUNT and AVG on a sensor network. Due to power and range constraints, centralized approaches are generally impractical, so most systems use in-network aggregation to reduce network traffic. However, these aggregation strategies become bandwidth-intensive when combined with the fault-tolerant, multipath routing methods often used in these environments. For example, duplicate-sensitive aggregates such as SUM cannot be computed exactly using substantially less bandwidth than explicit enumeration. To avoid this expense, we investigate the use of approximate in-network aggregation using small sketches. Our contributions are as follows: 1) we generalize well known duplicate-insensitive sketches for approximating COUNT to handle SUM, 2) we present and analyze methods for using sketches to produce accurate results with low communication and computation overhead, and 3) we present an extensive experimental validation of our methods.

On indexing mobile objects

We show how to index mobile objects in one and two dimensions using efficient dynamic external memory data structures. The problem is motivated by real life applications in traffic monitoring, intelligent navigation and mobile communications domains. For the l-dimensional case, we give (i) a dynamic, external memory algorithm with guaranteed worst case performance and linear space and (ii) a practical approximation algorithm also in the dynamic, external memory setting, which has linear space and expected logarithmic query time. We also give an algorithm with guaranteed logarithmic query time for a restricted version of the problem. We present extensions of our techniques to two dimensions. In addition we give a lower bound on the number of I/O’s needed to answer the d-dimensional problem. Initial experimental results and comparisons to traditional indexing approaches are also included.

Dynamic authenticated index structures for outsourced databases

In outsourced database (ODB)systems the database owner publishes its data through a number of remote servers, with the goal of enabling clients at the edge of the network to access and query the data more efficiently. As servers might be untrusted or can be compromised, query authentication becomes an essential component of ODB systems. Existing solutions for this problem concentrate mostly on static scenarios and are based on idealistic properties for certain cryptographic primitives. In this work, first we define a variety of essential and practical cost metrics associated with ODB systems. Then, we analytically evaluate a number of different approaches, in search for a solution that best leverages all metrics. Most importantly, we look at solutions that can handle dynamic scenarios, where owners periodically update the data residing at the servers. Finally, we discuss query freshness, a new dimension in data authentication that has not been explored before. A comprehensive experimental evaluation of the proposed and existing approaches is used to validate the analytical models and verify our claims. Our findings exhibit that the proposed solutions improve performance substantially over existing approaches, both for static and dynamic environments.

Mining, indexing, and querying historical spatiotemporal data

In many applications that track and analyze spatiotemporal data, movements obey periodic patterns; the objects follow the same routes (approximately) over regular time intervals. For example, people wake up at the same time and follow more or less the same route to their work everyday. The discovery of hidden periodic patterns in spatiotemporal data, apart from unveiling important information to the data analyst, can facilitate data management substantially. Based on this observation, we propose a framework that analyzes, manages, and queries object movements that follow such patterns. We define the spatiotemporal periodic pattern mining problem and propose an effective and fast mining algorithm for retrieving maximal periodic patterns. We also devise a novel, specialized index structure that can benefit from the discovered patterns to support more efficient execution of spatiotemporal queries. We evaluate our methods experimentally using datasets with object trajectories that exhibit periodicity.

MRShare: sharing across multiple queries in MapReduce

Large-scale data analysis lies in the core of modern enterprises and scientific research. With the emergence of cloud computing, the use of an analytical query processing infrastructure (e.g., Amazon EC2) can be directly mapped to monetary value. MapReduce has been a popular framework in the context of cloud computing, designed to serve long running queries (jobs) which can be processed in batch mode. Taking into account that different jobs often perform similar work, there are many opportunities for sharing. In principle, sharing similar work reduces the overall amount of work, which can lead to reducing monetary charges incurred while utilizing the processing infrastructure. In this paper we propose a sharing framework tailored to MapReduce. Our framework, MRShare, transforms a batch of queries into a new batch that will be executed more efficiently, by merging jobs into groups and evaluating each group as a single query. Based on our cost model for MapReduce, we define an optimization problem and we provide a solution that derives the optimal grouping of queries. Experiments in our prototype, built on top of Hadoop, demonstrate the overall effectiveness of our approach and substantial savings.

Approximating multi-dimensional aggregate range queries over real attributes

Finding approximate answers to multi-dimensional range queries over real valued attributes has significant applications in data exploration and database query optimization. In this paper we consider the following problem: given a table of d attributes whose domain is the real numbers, and a query that specifies a range in each dimension, find a good approximation of the number of records in the table that satisfy the query. We present a new histogram technique that is designed to approximate the density of multi-dimensional datasets with real attributes. Our technique finds buckets of variable size, and allows the buckets to overlap. Overlapping buckets allow more efficient approximation of the density. The size of the cells is based on the local density of the data. This technique leads to a faster and more compact approximation of the data distribution. We also show how to generalize kernel density estimators, and how to apply them on the multi-dimensional query approximation problem. Finally, we compare the accuracy of the proposed techniques with existing techniques using real and synthetic datasets.

Efficient Indexing of Spatiotemporal Objects

Spatiotemporal objects i.e., objects which change their position and/or extent over time, appear in many applications. This paper addresses the problem of indexing large volumes of such data. We consider general object movements and extent changes. We further concentrate on snapshot as well as small interval historical queries on the gathered data. The obvious approach that approximates spatiotemporal objects with MBRs and uses a traditional multidimensional access method to index them is inefficient. Objects that live for long time intervals have large MBRs which introduce a lot of empty space. Clustering long intervals has been dealt in temporal databases by the use of partially persistent indices. What differentiates this problem from traditional temporal indexing is that objects are allowed to move/change during their lifetime. Better methods are thus needed to approximate general spatiotemporal objects. One obvious solution is to introduce artificial splits: the lifetime of a long-lived object is split into smaller consecutive pieces. This decreases the empty space but increases the number of indexed MBRs. We first introduce two algorithms for splitting a given spatiotemporal object. Then, given an upper bound on the total number of possible splits, we present three algorithms that decide how the splits should be distributed among the objects so that the total empty space is minimized.

Non-linear dimensionality reduction techniques for classification and visualization

In this paper we address the issue of using local embeddings for data visualization in two and three dimensions, and for classification. We advocate their use on the basis that they provide an efficient mapping procedure from the original dimension of the data, to a lower intrinsic dimension. We depict how they can accurately capture the users perception of similarity in high-dimensional data for visualization purposes. Moreover, we exploit the low-dimensional mapping provided by these embeddings, to develop new classification techniques, and we show experimentally that the classification accuracy is comparable (albeit using fewer dimensions) to a number of other classification procedures.

k-nearest neighbors in uncertain graphs

Complex networks, such as biological, social, and communication networks, often entail uncertainty, and thus, can be modeled as probabilistic graphs. Similar to the problem of similarity search in standard graphs, a fundamental problem for probabilistic graphs is to efficiently answer k-nearest neighbor queries (k-NN), which is the problem of computing the k closest nodes to some specific node. In this paper we introduce a framework for processing k-NN queries in probabilistic graphs. We propose novel distance functions that extend well-known graph concepts, such as shortest paths. In order to compute them in probabilistic graphs, we design algorithms based on sampling. During k-NN query processing we efficiently prune the search space using novel techniques. Our experiments indicate that our distance functions outperform previously used alternatives in identifying true neighbors in real-world biological data. We also demonstrate that our algorithms scale for graphs with tens of millions of edges.