Continuous Nearest Neighbor Queries over Sliding Windows

Abstract—This paper studies continuous monitoring of nearest neighbor (NN) queries over sliding window streams. According to this model, data points continuously stream in the system, and they are considered valid only while they belong to a sliding window that contains 1) the W most recent arrivals (count-based) or 2) the arrivals within a fixed interval W covering the most recent time stamps (time-based). The task of the query processor is to constantly maintain the result of long-running NN queries among the valid data. We present two processing techniques that apply to both count-based and time-based windows. The first one adapts conceptual partitioning, the best existing method for continuous NN monitoring over update streams, to the sliding window model. The second technique reduces the problem to skyline maintenance in the distance-time space and precomputes the future changes in the NN set. We analyze the performance of both algorithms and extend them to variations of NN search. Finally, we compare their efficiency through a comprehensive experimental evaluation. The skyline-based algorithm achieves lower CPU cost, at the expense of slightly larger space overhead. Index Terms—Location-dependent and sensitive, spatial databases, query processing, nearest neighbors, data streams, sliding windows.

On trip planning queries in spatial databases

In this paper we discuss a new type of query in Spatial Databases, called Trip Planning Query (TPQ). Given a set of points P in space, where each point belongs to a category, and given two points s and e, TPQ asks for the best trip that starts at s, passes through exactly one point from each category, and ends at e. An example of a TPQ is when a user wants to visit a set of different places and at the same time minimize the total travelling cost, e.g. what is the shortest travelling plan for me to visit an automobile shop, a CVS pharmacy outlet, and a Best Buy shop along my trip from A to B? The trip planning query is an extension of the well-known TSP problem and therefore is NP-hard. The difficulty of this query lies in the existence of multiple choices for each category. In this paper, we first study fast approximation algorithms for the trip planning query in a metric space, assuming that the data set fits in main memory, and give the theory analysis of their approximation bounds. Then, the trip planning query is examined for data sets that do not fit in main memory and must be stored on disk. For the disk-resident data, we consider two cases. In one case, we assume that the points are located in Euclidean space and indexed with an Rtree. In the other case, we consider the problem of points that lie on the edges of a spatial network (e.g. road network) and the distance between two points is defined using the shortest distance over the network. Finally, we give an experimental evaluation of the proposed algorithms using synthetic data sets generated on real road networks

Approximate Nearest Neighbor Search for Low Dimensional Queries

We study the Approximate Nearest Neighbor problem for metric spaces where the query points are constrained to lie on a subspace of low doubling dimension, while the data is high-dimensional. We show that this problem can be solved efficiently despite the high dimensionality of the data.Comment: 25 page

On trip planning queries in spatial databases

In this paper we discuss a new type of query in Spatial Databases, called Trip Planning Query (TPQ). Given a set of points P in space, where each point belongs to a category, and given two points s and e, TPQ asks for the best trip that starts at s, passes through exactly one point from each category, and ends at e. An example of a TPQ is when a user wants to visit a set of different places and at the same time minimize the total travelling cost, e.g. what is the shortest travelling plan for me to visit an automobile shop, a CVS pharmacy outlet, and a Best Buy shop along my trip from A to B? The trip planning query is an extension of the well-known TSP problem and therefore is NP-hard. The difficulty of this query lies in the existence of multiple choices for each category. In this paper, we first study fast approximation algorithms for the trip planning query in a metric space, assuming that the data set fits in main memory, and give the theory analysis of their approximation bounds. Then, the trip planning query is examined for data sets that do not fit in main memory and must be stored on disk. For the disk-resident data, we consider two cases. In one case, we assume that the points are located in Euclidean space and indexed with an Rtree. In the other case, we consider the problem of points that lie on the edges of a spatial network (e.g. road network) and the distance between two points is defined using the shortest distance over the network. Finally, we give an experimental evaluation of the proposed algorithms using synthetic data sets generated on real road networks