Johannes Niedermayer

Probabilistic nearest neighbor queries on uncertain moving object trajectories

Nearest neighbor (NN) queries in trajectory databases have received significant attention in the past, due to their applications in spatio-temporal data analysis. More recent work has considered the realistic case where the trajectories are uncertain; however, only simple uncertainty models have been proposed, which do not allow for accurate probabilistic search. In this paper, we fill this gap by addressing probabilistic nearest neighbor queries in databases with uncertain trajectories modeled by stochastic processes, specifically the Markov chain model. We study three nearest neighbor query semantics that take as input a query state or trajectory q and a time interval, and theoretically evaluate their runtime complexity. Furthermore we propose a sampling approach which uses Bayesian inference to guarantee that sampled trajectories conform to the observation data stored in the database. This sampling approach can be used in Monte-Carlo based approximation solutions. We include an extensive experimental study to support our theoretical results.

Reverse-Nearest Neighbor Queries on Uncertain Moving Object Trajectories

Reverse nearest neighbor (RNN) queries in spatial and spatio-temporal databases have received significant attention in the database research community over the last decade. A reverse nearest neighbor (RNN) query finds the objects having a given query object as its nearest neighbor. RNN queries find applications in data mining, marketing analysis, and decision making. Most previous research on RNN queries over trajectory databases assume that the data are certain. In realistic scenarios, however, trajectories are inherently uncertain due to measurement errors or time-discretized sampling. In this paper, we study RNN queries in databases of uncertain trajectories. We propose two types of RNN queries based on a well established model for uncertain spatial temporal data based on stochastic processes, namely the Markov model. To the best of our knowledge our work is the first to consider RNN queries on uncertain trajectory databases in accordance with the possible worlds semantics. We include an extensive experimental evaluation on both real and synthetic data sets to verify our theoretical results.

On reverse-k-nearest-neighbor joins

A reverse k-nearest neighbour (RkNN) query determines the objects from a database that have the query as one of their k-nearest neighbors. Processing such a query has received plenty of attention in research. However, the effect of running multiple RkNN queries at once (join) or within a short time interval (bulk/group query) has only received little attention so far. In this paper, we analyze different types of RkNN joins and provide a classification of existing RkNN join algorithms. We discuss possible solutions for solving the non-trivial variants of the problem in vector spaces, including self and mutual pruning strategies. Further, we generalize the developed algorithms to general metric spaces. During an extensive performance analysis we provide evaluation results showing the IO and CPU performance of the compared algorithms for a wide range of different setups and suggest appropriate query algorithms for specific scenarios.

Monochromatic RkNN queries in time-dependent road networks

The problem of finding influence sets for a specific point, e.g. determining the influence of a location for a new restaurant on competitive restaurants, can be modeled as the reverse k nearest neighbor (RkNN) query. Although a lot of research has already been published on this topic, there is no adequate solution to solve the problem in time-dependent networks. In this work, we address RkNN queries in networks considering time-dependency, e.g. in road networks where traffic conditions influence the travel speed. Due to that the reverse nearest neighbors set can change over time, even if the objects are assumed to be static. We present an algorithm that solves the monochromatic time-dependent RkNN problem efficiently for a specific point in time. This algorithm uses a pruning technique to minimize the necessary network expansion. Furthermore, we present a variant of the algorithm which uses apriori knowledge from a pre-processing step to save further network expansion. Finally, we compare the proposed methods for monochromatic queries to a simple baseline approach by using time-dependent road networks of different sizes, various densities for the points of interests and various values for k. The results show that our proposed algorithms are orders of magnitude faster than a straightforward alternative.

Reverse-k-Nearest-Neighbor join processing

A reverse k-nearest neighbour (RkNN) query determines the objects from a database that have the query as one of their k-nearest neighbors. Processing such a query has received plenty of attention in research. However, the effect of running multiple RkNN queries at once (join) or within a short time interval (bulk/group query) has only received little attention so far. In this paper, we analyze different types of RkNN joins and discuss possible solutions for solving the non-trivial variants of this problem, including self and mutual pruning strategies. The results indicate that even with a moderate number of query objects (|R|≈0.0007|S|), the performance (CPU) of the state-of-the-art mutual pruning based RkNN-queries deteriorates and hence algorithms based on self pruning without precomputation produce better results. During an extensive performance analysis we provide evaluation results showing the IO and CPU performance of the compared algorithms for a wide range of different setups and suggest appropriate query algorithms for specific scenarios.

Exploration of monte-carlo based probabilistic query processing in uncertain graphs

This demo presents a framework for running probabilistic graph queries on uncertain graphs and visualizing their results. The framework supports the most common uncertainty model for uncertain graphs, i.e. existential uncertainty for the edges of the graph. A large variety of meaningful graph queries are supported, such as shortest path, range, kN, reverse kN, reachability and various aggregation queries. Since the problem of exact probability computation according to possible world semantics is in #P-Time for many combinations of model and query, and since ignoring uncertainty (e.g. by using expectations only) will yield counterintuitive and hard to interpret results, our framework uses an optimized version of Monte-Carlo sampling to estimate the results which allows us not only to perform queries that conform to possible world semantics but also to sample only parts of a graph relevant for a given query. The main strength of this framework is the visualization combined with statistic hypothesis tests, which gives the user not only the estimated result of a query, but also an indication of how significant and reliable these results are. The aim of this demonstration is to give an intuition that a sampling based approach to probabilistic graphs is viable, and that the estimated results quickly converge even for very large graphs. A video demonstrating our framework can be downloaded at http://www.dbs.ifi.lmu.de/Publikationen/videos/PGraph.html

An adaptive refinement-based algorithm for median queries in wireless sensor networks

A number of papers concerning algorithms for processing typical aggregate queries, e.g., Max and Top-k, within a wireless sensor network have been published in recent years. However, relatively few have addressed Median queries. In this paper we propose an exact algorithm to process Median queries that is based on a series of refinement queries. Each refinement query is a Histogram query, with the aim of incrementally refining the range where the actual median value resides. Because the cost of a Histogram query depends mostly on the structure of the histogram itself, we aim at optimizing each Histogram query, hence optimizing the overall cost of the Median query. Experiments, using synthetic and real datasets, show that our proposed approach yields up to 50% less traffic than a TAG-based solution and only about 25% more traffic on average than the minimum required.

Similarity Search on Uncertain Spatio-temporal Data

In this work, we address the problem of similarity search in a database of uncertain spatio-temporal objects. Each object is defined by a set of observations time,location-tuples and a Markov chain which describes the objects uncertain motion in space and time. To model similarity - which is an important building block for many applications such as identifying frequent motion patterns or trajectory clustering - we employ the well-known Longest Common Subsequence LCSS measure, which becomes a distribution on uncertain spatio-temporal data ULCSS. We show how the aligned version without time shifting of the ULCSS can be exactly computed in PTIME, which is also verified by extensive experiments.

Cost-Based Quantile Query Processing in Wireless Sensor Networks

In this paper we investigate how to efficiently and effectively use histogram queries for processing quantile queries in wireless sensor networks. A major concern when processing queries within such an environment is to minimize the energy consumption by the network nodes, thus extending the networks lifetime, e.g., the time when the first node runs out of energy. Towards that goal, we define a cost model for a refinement-based algorithm that performs a series of refining histogram queries in order to determine the exact quantile value. Given that the histogram size, i.e., its number of bins, is an important factor in the query processing cost, we use the defined cost model to estimate the histogram size that minimizes the maximum energy cost per-node when processing the quantile query. This is equivalent to maximizing the time until the first node dies and therefore to extending the networks lifetime. In our experiments, using synthetic and real datasets, we evaluate the performance of the proposed solutions in a variety of different settings.

Minimizing the Number of Keypoint Matching Queries for Object Retrieval.

To increase the efficiency of interest-point based object retrieval, researchers have put remarkable research efforts into improving the efficiency of kNN-based feature matching, pursuing to match thousands of features against a database within fractions of a second. However, due to the high-dimensional nature of image features that reduces the effectivity of index structures (curse of dimensionality) and due to the vast amount of features stored in image databases (images are often represented by up to several thousand features), this ultimate goal demanded to trade kNN query runtimes for query precision. In this paper we address an approach complementary to indexing in order to improve the efficiency of retrieval by querying only the most promising keypoint descriptors, as this affects kNN matching time linearly. As this reduction of kNN queries reduces the number of tentative correspondences, a loss of query precision is minimized by an additional image-level correspondence generation stage with a computational performance independent of the underlying indexing structure. Our experimental evaluation suggests good performance on a variety of datasets.