154
Chapter IX
eDAR Algorithm for
Continuous KNN Queries
Based on Pine
Maytham Safar
Kuwait University, Kuwait
Dariush Ebrahimi
Kuwait University, Kuwait
Abstract
The continuous K nearest neighbor (CKNN) query is an important type of query that finds continuously
the KNN to a query point on a given path. We focus on moving queries issued on stationary objects in
Spatial Network Database (SNDB) The result of this type of query is a set of intervals (defined by split
points) and their corresponding KNNs. This means that the KNN of an object traveling on one interval
of the path remains the same all through that interval, until it reaches a split point where its KNNs
change. Existing methods for CKNN are based on Euclidean distances. In this paper we propose a new
algorithm for answering CKNN in SNDB where the important measure for the shortest path is network
distances rather than Euclidean distances. We propose DAR and eDAR algorithms to address CKNN
queries based on the progressive incremental network expansion (PINE) technique. Our experiments
show that the eDAR approach has better response time, and requires fewer shortest distance computations and KNN queries than approaches that are based on VN3 using IE.
Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited.
eDAR Algorithm for Continuous KNN Queries Based on Pine
INTRODUCTION
Several types of nearest neighbor (NN) search
algorithms have been proposed and studied in the
context of spatial databases. The most common
type is the point KNN query, which is defined as:
given a set of spatial objects (or points of interest),
and an input query point, retrieve the (K) nearest
neighbors to that query point. The NN is the target
object with the shortest path from the query point
on the route. The efficient implementation of KNN
query is of a particular interest in geographical
information systems (GIS). For example, a GPS
device in a vehicle gives information of an object’s
location, which, once located onto a map, serves
as a basis to find the K closest restaurants or gas
stations with the shortest path to them.
Different variations of KNN queries have been
introduced. One variation is the continuous KNNs
of any point on a given path. As an example, when
the GPS device of the vehicle initiates a query to
continuously find the three nearest gas stations
to the vehicle at any point of a path from source
to destination. The result is a set of intervals or
split points where the KNNs of a moving object
on a path will be the same up to these points. The
versatility of K nearest neighbors search increases
substantially if we consider other variations of it
such as the continuous KNN (CKNN). CKNN
query is defined as the K nearest point of interest
to every point on a path, and has found applications in the GISs (e.g., find my nearest three gas
stations at any point during my route from city
A to city B). The result of this type of query is
a set of tuples <result, interval> such that result
is the KNN of all points in the corresponding
interval ordered by distances to the query point.
The interval is defined by two end-points called
split points, which specify where on the path
the KNNs of a moving object will change. This
means that the KNNs of an object traveling in one
interval of the path remain the same all through
that interval until it reaches a split point where
its KNNs change.
In spatial network databases, as well as in
practice, objects are restricted to move only on a
predefined set of paths as specified by the underlying network (road, railroad, river, etc.) Thus, the
network distance (i.e., the length of the shortest
path connecting two objects is what represents the
real distance between objects and not the objects’
relative position in space). Surprisingly, most of
the existing work considers only the Cartesian
(Euclidean) spaces where the path between two
objects is the straight line connecting them, which
renders the distance computation impractical for
spatial network databases (SNDBs.)
Our objects are restricted to move on pre-defined paths (e.g., road) that are specified by an
underlying network. This means that the shortest network path (distance) between the objects
(e.g., the vehicle and the gas station) depends on
the connectivity of the network rather than the
objects locations. In Safar (2005), we proposed a
Voronoi-based progressive incremental network
expansion (PINE) technique to solve the KNN
queries. The main idea behind PINE is to first
partition a large network into smaller regions by
generating a network Voronoi diagram over the
points of interest. Each cell of this Voronoi diagram
is centered by one object (e.g., restaurant) and
contains the nodes that are closest to that object
in network distance. Next, we pre-compute the
inter distances for each cell (i.e., distances across
the border points of the adjacent cells). This would
later reduce the pre-computation time and space
to answer KNN queries. To find the first nearest
neighbours of a query object, we find the first
nearest neighbour by simply locating the Voronoi
cell that contains the query object, then starting
from the query point, we perform network expansion by computing the distance from our query to
its first nearest neighbour (its Voronoi cell center
point) and exploring the objects that are close to
the query object then computing their distances to
the query object during the expansion. In PINE,
at the first scale inside the Voronoi cell, which
contains the query object, the network expansion
155
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