Mehdi Sharifzadeh

A Road Network Embedding Technique for K-Nearest Neighbor Search in Moving Object Databases

A very important class of queries in GIS applications is the class of K-nearest neighbor queries. Most of the current studies on the K-nearest neighbor queries utilize spatial index structures and hence are based on the Euclidean distances between the points. In real-world road networks, however, the shortest distance between two points depends on the actual path connecting the points and cannot be computed accurately using one of the Minkowski metrics. Thus, the Euclidean distance may not properly approximate the real distance. In this paper, we apply an embedding technique to transform a road network to a high dimensional space in order to utilize computationally simple Minkowski metrics for distance measurement. Subsequently, we extend our approach to dynamically transform new points into the embedding space. Finally, we propose an efficient technique that can find the actual shortest path between two points in the original road network using only the embedding space. Our empirical experiments indicate that the Chessboard distance metric (L∞) in the embedding space preserves the ordering of the distances between a point and its neighbors more precisely as compared to the Euclidean distance in the original road network.

The optimal sequenced route query

Real-world road-planning applications often result in the formulation of new variations of the nearest neighbor (NN) problem requiring new solutions. In this paper, we study an unexplored form of NN queries named optimal sequenced route (OSR) query in both vector and metric spaces. OSR strives to find a route of minimum length starting from a given source location and passing through a number of typed locations in a particular order imposed on the types of the locations. We first transform the OSR problem into a shortest path problem on a large planar graph. We show that a classic shortest path algorithm such as Dijkstra’s is impractical for most real-world scenarios. Therefore, we propose LORD, a light threshold-based iterative algorithm, which utilizes various thresholds to prune the locations that cannot belong to the optimal route. Then we propose R-LORD, an extension of LORD which uses R-tree to examine the threshold values more efficiently. Finally, for applications that cannot tolerate the Euclidean distance as estimation and require exact distance measures in metric spaces (e.g., road networks) we propose PNE that progressively issues NN queries on different point types to construct the optimal route for the OSR query. Our extensive experiments on both real-world and synthetic datasets verify that our algorithms significantly outperform a disk-based variation of the Dijkstra approach in terms of processing time (up to two orders of magnitude) and required workspace (up to 90% reduction on average).

A road network embedding technique for k-nearest neighbor search in moving object databases

A very important class of queries in GIS applications is the class of K-Nearest Neighbor queries. Most of the current studies on the K-Nearest Neighbor queries utilize spatial index structures and hence are based on the Euclidean distances between the points. In real-world road networks, however, the shortest distance between two points depends on the actual path connecting the points and cannot be computed accurately using one of the Minkowski metrics. Thus, the Euclidean distance may not properly approximate the real distance. In this paper, we apply an embedding technique to transform a road network to a high dimensional space in order to utilize computationally simple Minkowski metrics for distance measurement. Subsequently, we extend our approach to dynamically transform new points into the embedding space. Finally, we propose an efficient technique that can find the actual shortest path between two points in the original road network using only the embedding space. Our empirical experiments indicate that the Chessboard distance metric (∞) in the embedding space preserves the ordering of the distances between a point and its neighbors more precisely as compared to the Euclidean distance in the original road network.

VoR-tree: R-trees with Voronoi diagrams for efficient processing of spatial nearest neighbor queries

A very important class of spatial queries consists of nearest-neighbor (NN) query and its variations. Many studies in the past decade utilize R-trees as their underlying index structures to address NN queries efficiently. The general approach is to use R-tree in two phases. First, R-trees hierarchical structure is used to quickly arrive to the neighborhood of the result set. Second, the R-tree nodes intersecting with the local neighborhood (Search Region) of an initial answer are investigated to find all the members of the result set. While R-trees are very efficient for the first phase, they usually result in the unnecessary investigation of many nodes that none or only a small subset of their including points belongs to the actual result set. On the other hand, several recent studies showed that the Voronoi diagrams are extremely efficient in exploring an NN search region, while due to lack of an efficient access method, their arrival to this region is slow. In this paper, we propose a new index structure, termed VoR-Tree that incorporates Voronoi diagrams into R-tree, benefiting from the best of both worlds. The coarse granule rectangle nodes of R-tree enable us to get to the search region in logarithmic time while the fine granule polygons of Voronoi diagram allow us to efficiently tile or cover the region and find the result. Utilizing VoR-Tree, we propose efficient algorithms for various Nearest Neighbor queries, and show that our algorithms have better I/O complexity than their best competitors.

Processing spatial skyline queries in both vector spaces and spatial network databases

In this article, we first introduce the concept of Spatial Skyline Queries (SSQ). Given a set of data points <i>P</i> and a set of query points <i>Q</i>, each data point has a number of <i>derived spatial</i> attributes each of which is the points distance to a query point. An SSQ retrieves those points of <i>P</i> which are not dominated by any other point in <i>P</i> considering their derived spatial attributes. The main difference with the regular skyline query is that this <i>spatial domination</i> depends on the location of the query points <i>Q</i>. SSQ has application in several domains such as emergency response and online maps. The main intuition and novelty behind our approaches is that we exploit the geometric properties of the SSQ problem space to avoid the exhaustive examination of all the point pairs in <i>P</i> and <i>Q</i>. Consequently, we reduce the complexity of SSQ search from <i>O</i>(|<i>P</i>|²|<i>Q</i>|) to <i>O</i>(|<i>S</i>|²|<i>C</i>| + &sqrt;|<i>P</i>|), where |<i>S</i>| and |<i>C</i>| are the solution size and the number of vertices of the convex hull of <i>Q</i>, respectively. Considering Euclidean distance, we propose two algorithms, B²S² and VS², for static query points and one algorithm, VCS², for streaming <i>Q</i> whose points change location over time (e.g., are mobile). VCS² exploits the pattern of change in <i>Q</i> to avoid unnecessary recomputation of the skyline and hence efficiently perform updates. We also propose two algorithms, SNS² and VSNS², that compute the spatial skyline with respect to the network distance in a spatial network database. Our extensive experiments using real-world datasets verify that both R-tree-based B²S² and Voronoi-based VS² outperform the best competitor approach in terms of both processing time and I/O cost. Furthermore, their output computed based on Euclidean distance is a good approximation of the spatial skyline in network space. For accurate computation of spatial skylines in network space, our experiments showed the superiority of VSNS² over SNS².

Change detection in time series data using wavelet footprints

In this paper, we propose a novel approach to address the problem of change detection in time series data. Our approach is based on wavelet footprints proposed originally by the signal processing community for signal compression. We, however, exploit the properties of footprints to capture discontinuities in a signal. We show that transforming data using footprints generates nonzero coefficients only at the change points. Exploiting this property, we propose a change detection query processing scheme which employs footprint-transformed data to identify change points, their amplitudes, and degrees of change efficiently and accurately. Our analytical and empirical results show that our approach outperforms the best known change detection approach in terms of both performance and accuracy. Furthermore, unlike the state of the art approaches, our query response time is independent of the number of change points and the user-defined change threshold.

Processing Optimal Sequenced Route Queries Using Voronoi Diagrams

The Optimal Sequenced Route (OSR) query strives to find a route of minimum length starting from a given source location and passing through a number of typed locations in a specific sequence imposed on the types of the locations. In this paper, we propose a pre-computation approach to OSR query in both vector and metric spaces. We exploit the geometric properties of the solution space and theoretically prove its relation to additively weighted Voronoi diagrams. Our approach recursively accesses these diagrams to incrementally build the OSR. Introducing the analogous diagrams for the space of road networks, we show that our approach is also efficiently applicable to this metric space. Our experimental results verify that our pre-computation approach outperforms the previous index-based approaches in terms of query response time.

Utilizing Voronoi Cells of Location Data Streams for Accurate Computation of Aggregate Functions in Sensor Networks

Sensor networks are unattended deeply distributed systems whose database schema can be conceptualized using the relational model. Aggregation queries on the data sampled at each sensor node are the main means to extract the abstract characteristics of the surrounding environment. However, the non-uniform distribution of the sensor nodes in the environment leads to inaccurate results generated by the aggregation queries. In this paper, we introduce “spatial aggregations” that take into consideration the spatial location of each measurement generated by the sensor nodes. We propose the use of spatial interpolation methods derived from the fields of spatial statistics and computational geometry to answer spatial aggregations. In particular, we study Spatial Moving Average (SMA), Voronoi Diagram and Triangulated Irregular Network (TIN). Investigating these methods for answering spatial average queries, we show that the average value on the data samples weighted by the area of the Voronoi cell of the corresponding sensor node, provides the best precision. Consequently, we introduce an algorithms to compute and maintain the accurate Voronoi cell at each sensor node while the location of the others arrive on data stream. We also propose AVC-SW, a novel algorithm to approximate this Voronoi cell over a sliding window that supports dynamism in the sensor network. To demonstrate the performance of in-network implementation of our aggregation operators, we have developed prototypes of two different approaches to distributed spatial aggregate processing.

A hybrid aggregation and compression technique for road network databases

Vector data and in particular road networks are being queried, hosted and processed in many application domains such as in mobile computing. Many client systems such as PDAs would prefer to receive the query results in unrasterized format without introducing an overhead on overall system performance and result size. While several general vector data compression schemes have been studied by different communities, we propose a novel approach in vector data compression which is easily integrated within a geospatial query processing system. It uses line aggregation to reduce the number of relevant tuples and Huffman compression to achieve a multi-resolution compressed representation of a road network database. Our experiments performed on an end-to-end prototype verify that our approach exhibits fast query processing on both client and server sides as well as high compression ratio.

Optimal traversal planning in road networks with navigational constraints

A frequent query in geospatial planning and decision making domains (e.g., emergency response, data acquisition, street cleaning), is to find an optimal traversal plan (OTP) that traverses an entire area (e.g., a city) by navigating through all its streets. The optimality is defined in terms of the time it takes to complete the traversal. This time depends on the number of times each street segment is traversed as well as the navigation time such as the time spent on changing direction at each intersection. While the problem roots in the classic problems of graph theory, real-world geospatial constraints of road network introduce new application-specific challenges. In this paper, we propose two algorithms to find OTP of a directed road network. Our greedy algorithm employs a classic graph traversal algorithm. During the traversal, it utilizes a set of heuristics at each intersection to minimize the total travel time. Our near-optimal algorithm, however, reduces an OTP problem to an Asymmetric Traveling Salesman Problem (ATSP) by extracting the dual graph of the original network in which each edge is represented by a graph node. Using an approximate solution for ATSP, our algorithm finds a near optimal answer. Our experiments using real-world road networks verify that our near-optimal algorithm outperforms the greedy algorithm in terms of the overall cost of its generated traversal by a factor of two, while its complexity is tolerable in real-world cases.