9,271 research outputs found
Analysis of approximate nearest neighbor searching with clustered point sets
We present an empirical analysis of data structures for approximate nearest
neighbor searching. We compare the well-known optimized kd-tree splitting
method against two alternative splitting methods. The first, called the
sliding-midpoint method, which attempts to balance the goals of producing
subdivision cells of bounded aspect ratio, while not producing any empty cells.
The second, called the minimum-ambiguity method is a query-based approach. In
addition to the data points, it is also given a training set of query points
for preprocessing. It employs a simple greedy algorithm to select the splitting
plane that minimizes the average amount of ambiguity in the choice of the
nearest neighbor for the training points. We provide an empirical analysis
comparing these two methods against the optimized kd-tree construction for a
number of synthetically generated data and query sets. We demonstrate that for
clustered data and query sets, these algorithms can provide significant
improvements over the standard kd-tree construction for approximate nearest
neighbor searching.Comment: 20 pages, 8 figures. Presented at ALENEX '99, Baltimore, MD, Jan
15-16, 199
Reverse k Nearest Neighbor Search over Trajectories
GPS enables mobile devices to continuously provide new opportunities to
improve our daily lives. For example, the data collected in applications
created by Uber or Public Transport Authorities can be used to plan
transportation routes, estimate capacities, and proactively identify low
coverage areas. In this paper, we study a new kind of query-Reverse k Nearest
Neighbor Search over Trajectories (RkNNT), which can be used for route planning
and capacity estimation. Given a set of existing routes DR, a set of passenger
transitions DT, and a query route Q, a RkNNT query returns all transitions that
take Q as one of its k nearest travel routes. To solve the problem, we first
develop an index to handle dynamic trajectory updates, so that the most
up-to-date transition data are available for answering a RkNNT query. Then we
introduce a filter refinement framework for processing RkNNT queries using the
proposed indexes. Next, we show how to use RkNNT to solve the optimal route
planning problem MaxRkNNT (MinRkNNT), which is to search for the optimal route
from a start location to an end location that could attract the maximum (or
minimum) number of passengers based on a pre-defined travel distance threshold.
Experiments on real datasets demonstrate the efficiency and scalability of our
approaches. To the best of our best knowledge, this is the first work to study
the RkNNT problem for route planning.Comment: 12 page
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