Efficiently Querying Moving Objects with Pre-defined
Paths in a Distributed Environment
∗
Cyrus Shahabi, Mohammad R. Kolahdouzan, Snehal Thakkar,
Jose Luis Ambite
†
and Craig A. Knoblock
†
Department of Computer Science and
†
Information Sciences Institute
University of Southern California
Los Angeles, California 90089
[shahabi, kolahdoz, snehalth]@usc.edu [ambite, knoblock]@isi.edu
ABSTRACT
Due to the recent growth of the World Wide Web, numer-
ous spatio-temp oral applications can obtain their required
information from publicly available web sources. We con-
sider those sources maintaining moving objects with prede-
fined paths and schedules, and investigate different plans to
p erform queries on the integration of these data sources effi-
ciently. Examples of such data sources are networks of rail-
road paths and schedules for trains running between cities
connected through these networks. A typical query on such
data sources is to find all trains that pass through a given
p oint on the network within a given time interval. We show
that traditional filter+semi-join plans would not result in ef-
ficient query response times on distributed spatio-temporal
sources. Hence, we propose a novel spatio-temp oral filter,
called deviation filter, that exploits both the spatial and tem-
p oral characteristics of the sources in order to improve the
selectivity. We also report on our experiments in comparing
the performances of the alternative query plans and con-
clude that the plan with spatio-temp oral filter is the most
viable and superior plan.
1. INTRODUCTION
The explosive growth of the Internet has made a wealth
of networked information available. Much of this informa-
tion is geographical, spatial, temporal, or pertains to ob-
jects that have a spatial or temporal nature. The sources
of this information are heterogeneous: traditional databases
∗
This research has been funded in part by NSF grants EEC-
9529152 (IMSC ERC) and ITR-0082826, NASA/JPL con-
tract nr. 961518, DARPA and USAF under agreement nr.
F30602-99-1-0524, and unrestricted cash/equipment gifts
from NCR, IBM, Intel and SUN.
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with spatial extensions, geographical information systems
(GIS) software packages, mapping and imagery web sites,
web sites with spatial information, etc. An increasing num-
ber of web sites have information of a geospatial or temporal
character. For example, detailed satellite images can be ob-
tained from sites such as www.terraserver.com; maps from
www.mapquest.com; train schedules from www.amtrak.com;
geolocated points of interest such as train stations from
www.usgs.gov; geographical features such as railroad net-
works from www.nima.mil ; etc. The number of sources,
the quality, and detail of the information available are con-
tinually growing all around the globe. In this paper, we
focus our attention on how to efficiently query moving ob-
jects such as trains in a distributed environment such as the
one mentioned above.
Recently there has b een a growing interest in moving object
databases that manage the spatial objects whose position
changes over time [2, 3, 4, 5, 6, 7, 8]. Example applications
are those who query the locations of trains, cars and planes
for a given time interval. The main challenge investigated
by these studies is how to model the large spatio-temporal
data needed to track the position of any object at any given
time (either in the past, future or now).
In this paper, we consider an environment where the content
of the moving object database do es not need to be modi-
fied to reflect the movement of the objects. We term this
environment as “moving objects with predefined paths and
schedules.” An example application is to query the loca-
tion of trains moving on a railroad network. By storing
the schedules of trains’ departures and arrivals, the loca-
tions of the stations and the vector data corresponding to
the railroad network, we have enough information to query
the location of any moving object (i.e., train) at any given
time. Note that the database still needs to be modified (e.g.,
when schedule changes), but it does not need to be updated
(and/or appended) as the objects move around the network
within the provided schedule. The challenge, however, is
that queries of the type of finding the location of a train
in a given time interval are time consuming because of the
expensive functions such as the shortest path function that
need to be performed on large vector data as well as the
temp oral intersections that need to be applied on large sets
of time intervals.
One solution to reduce the query processing time of mov-
ing objects with predefined paths and schedules is to pre-
compute the required information and materialize it using
a moving object data model such as the 3D Trajectory [3]
mo del. This is a feasible approach if we assume that differ-
ent schedules, railroads and stations information are all local
and over which we have full control. However, with our as-
sumed distributed environment, the sources of information
that we would like to access are autonomous and dynamic.
That is, we do not have administrative control over them,
cannot modify their structure, or write data to them. The
sources can change their information without warning. Dif-
ferent sources may contain overlapping information or only
fragments of desired data.
Therefore, we propose alternative distributed query plans to
realize the integration of spatial and temporal information
(e.g., network of the railroads and schedules of the trains)
from distributed, heterogeneous sources. We start by in-
vestigating traditional filter+semi-join plans by either ap-
plying the temporal filter first and then perform the spa-
tial semi-join or vice versa. However, we show that there
are two main drawbacks with pure filter+semi-join plans.
First, spatial filters (e.g., identifying all railroad segments
that overlap with a given point) are computationally com-
plex resulting in long local or remote query processing time.
Second, temporal filters (identifying all intervals that over-
lap with a given interval) usually have bad selectivity due
to the large range of intervals covered by each instance in
the temporal source (e.g., schedule table). That is, many
schedules usually intersect with any query interval. Thus,
temp oral filters cannot effectively reduce the amount of data
transferred over the network. We try to overcome the first
obstacle by either performing a pre-computation step and
then apply a less expensive function/filter, or delaying the
spatial filter until we reduce the size of the spatial data (e.g.,
railroad vector data) significantly. We address the second
obstacle by proposing a spatio-temporal filter (termed de-
viation filter), instead of temporal-only filters, which can
also exploit the spatial characteristics of the data to im-
prove the selectivity. Finally, we report on our experiments
in evaluating and comparing the p erformances of our differ-
ent moving object query plans. Although one version of the
pre-computation approach outperforms all the other plans,
the pre-computation approach may not be feasible due to
limited control over remote sources. Therefore, we conclude
that our deviation based approach, which is only marginally
worse than the pre-computation approach, is the superior
plan.
The remainder of this paper is organized as follows. We
formally define the problem in Section 2. Sections 3 and 4
discuss the solutions to the problem for the centralized and
distributed environments, respectively. Section 5 reports on
our experimental observations. Finally, we discuss the con-
clusion and future work in Section 6.
2. PROBLEM DEFINITION
To better understand the problem, consider a scenario that
a movie is being produced at a certain location on a certain
date for several hours. The director of the movie needs to
make sure that no train passes by that location while they
are shooting the movie. This requires having information
about the schedules of the trains running on the nearby
railroads.
The following is the list of the simplified version of the
sources available on the web and in our local databases,
which can be used to provide necessary information for the
director of the movie.
• Name of the train stations and their geographical lo-
cations (from Silicon Mapping Solutions):
S
station
= Stations( Station-Name, Station-Point)
where station-name is a character string that contains
a unique name for each station and station-point rep-
resents the latitude and longitude of the station.
• Up-to-date schedule information of the trains (from
the train company web site):
S
schedule
= Schedules( Train-ID, Departing-Station-
Name, Departing-Time, Arriving-Station-Name, Arriving-
Time )
• The vector data containing the railroads’ path (from
Nima gazetter):
S
railroads
= Railroads( Railroad-ID, Railroad-Path,
Starting-Point, Ending-Point )
where the railroad-path is a 2D line with starting-point
and ending-point as its first and last vertices.
As a real-world example, the above sources of information
for the United States contain around 1000 stations, 400,000
schedules, and 170,000 line segments for the railroad net-
work. By appropriate spatio-temporal integration of the
above sources, we are interested in processing the following
types of queries:
• Q1: Find the position of a train for a given time in-
stant.
• Q2: Given a geographical point and a time interval,
find all the trains that pass through the point during
the given time interval.
For the reminder of this paper, to simplify the discussion,
we only focus on the more general query, i.e. Q2. We now
formally define the sources of information and predicates of
Q2 as:
• Name of the stations :
s = {(s
i
)|1 ≤ i ≤ N
s
} where N
s
is the total number of
stations.
• Locations of the stations:
S
stations
= {(s
i
, (x
i
, y
i
))|1 ≤ i ≤ N
s
} where (x
i
, y
i
)
sp ecify the geographical location of the station s
i
.
• Schedules of the trains:
S
schedules
= {V
k
|V
k
= (T rain
id
, s
i
, s
j
, [t
i
, t
j
])|1 ≤ i, j ≤
N
s
; 1 ≤ k ≤ M } where M is the cardinality of sched-
ules. Note that M À N
s
.
• Railroad network:
S
railroads
= {(< X
i
, Y
i
> ... < X
j
, Y
j
>)|1 ≤ i, j ≤
N
r
; (x
i
, y
i
)(X, Y )} where N
r
is the number of rail-
roads in the railroad network that is in the order of
N
2
s
, and (X, Y ) specifies the geographical location of
the starting and ending points of each railroad seg-
ment. Note that not all the start and end points are
stations. However, all stations are either a start or an
end point or both. Hence N
r
À N
s
.
S
1
S
4
S
6
V
2
V
3
V
5
L
1
L
2
L
3
L
4
L
5
S
7
L
6
L
7
Figure 1: An example of railroad networks
• Q
T
= Intersect([t
a
, t
b
], [t
i
, t
j
])
Q
T
, representing the temporal predicate of the query,
finds schedules that have intersection with a given time
interval [t
a
, t
b
].
• Q
S
= Intersect((x, y), Ψ(S
railroads
))
where Ψ(S
railroads
) is a function that calculates the
shortest
1
railroad paths between all possible start and
end point pairs (< X
i
, Y
i
>, < X
j
, Y
j
>).
• Q
0
S
= Intersect((x, y), Φ(S
railroads
, S
stations
))
where Φ(S
railroads
, S
stations
) is a function that calcu-
lates the shortest railroad paths between all station
pairs (< x
i
, y
i
>, < x
j
, y
j
>). Since the set of the sta-
tion coordinates, (x, y), is a small subset of the starting
and ending points in the railroad network, (X, Y ), the
Φ function is computationally less expensive than Ψ.
With Q
S
and Q
0
S
, it is not sufficient to only find those
line segments that intersect with (x, y), but subsequently
all the paths that include those segments. Hence, the func-
tion Ψ constructs all paths between any possible start and
end points (complexity O(N
2
r
)) while Φ does the same oper-
ation on all possible station pairs (complexity O(N
2
s
)). Dur-
ing this path construction, there may be cases where there
are more than one path between two points. In these cases,
b oth Ψ and Φ choose the shortest path, or actually never
construct the other paths.
To illustrate the difference between the functions Ψ and Φ
consider the following example:
Example 2.1.: Figure 1 illustrates a railroad network
with 7 starting and ending points, out of which 4 are stations
(S
1
, S
4
, S
6
, S
7
). Table 1 shows the results of applying the Ψ
and Φ functions to this network. Note that both functions
only compute the shortest path between the pair of points
among all possible paths. For example, there are two possible
paths between S
4
and S
7
. The path (L
3
, L
2
, L
7
) is computed,
while (L
4
, L
5
, L
6
) is discarded.
The sources S
stations
and S
railroads
contain spatial informa-
tion while S
schedules
has temporal content. Q
T
, Q
S
and Q
0
S
represent the temporal and spatial predicates of the query
Q2. Note that there are two alternative ways to evaluate
spatial part of the query using either Q
S
or Q
0
S
. Figure 2
depicts possible query plans to integrate the sources in a
distributed environment.
1
We assume that the trains travel through the shortest path
b etween two stations as it is true in the real-world applica-
tion.
Q
T
S
sche
dules
S
railr
oads
S
st
ations
Q
S
Q’
S
Deviation
Final Refinement Final Refinement
Server
1
Serve
r 2 Server 3
a. Joining stations and schedules first.
S
S
S
Q
T
Q
T
Q’
S
S
SPP
S
Q’
Pre-computation
st
ations
railr
oads
sche
dules
Final Refinement Final Refinement
Server
1
Serve
r 2 Server 3
b. Joining stations and railroads first.
Figure 2: Alternative query plans to integrate
sources in a distributed environment.
3. CENTRALIZED ENVIRONMENT
In this section, we briefly describe the solution to the prob-
lem described in Section 2 using a centralized environment.
We integrate the sources S
stations
, S
schedules
and S
railroads
off-line using the following relational algebra expression to
generate a 3D-trajectory source.
3D T rajectory(T rain ID, T rajectory) :=
(S
schedules
s
i
S
stations
)
<x
i
,y
i
>
S
railroads
(1)
We model each train as a moving point in 2D or equiva-
lently a line in 3D with time as its third dimension. With
this model, we can answer the queries described in Section 2
through an intersect operation on 3D-trajectory source be-
tween each train trajectory and (x, y, [t
a
, t
b
]), where (x, y) is
the query point and [t
a
, t
b
] is the given time interval. The
relational algebra expression for the intersect operation is
given in Equation 2. This approach has been used in the
moving objects literature.
σ
Intersect((x,y,[t
a
,t
b
]),T rajectory)
(3D T rajectory) (2)
There are disadvantages associated with the centralized ap-
proach. The cost of building the materialized view is usu-
ally very high as the sources usually contain large sets of
data. Furthermore, update and insert operations to the orig-
inal sources lead to expensive updates of the 3D trajectory
source. In addition, the limitations of the mediator server
and/or regulations imp osed by remote sources may restrict
us from materializing the data locally.
4. DISTRIBUTED ENVIRONMENT
In this section, we describe four alternative approaches to
integrate the sources S
stations
, S
schedules
and S
railroads
in a
Result of the Ψ function Result of the Φ function
(L
1
), (L
1
, L
2
), (L
1
, L
2
, L
3
), (L
1
, L
2
, L
3
, L
4
), (L
1
, L
7
, L
6
), (L
1
, L
7
) (L
1
, L
2
, L
3
), (L
1
, L
7
), (L
1
, L
7
, L
6
)
(L
2
), (L
2
, L
3
), (L
2
, L
3
, L
4
), (L
7
, L
6
), (L
7
) (L
3
, L
2
, L
7
), (L
4
, L
5
)
(L
3
), (L
3
, L
4
), (L
2
, L
7
, L
6
), (L
2
, L
7
) (L
6
)
(L
4
), (L
4
, L
5
), (L
3
, L
2
, L
7
)
(L
5
), (L
5
, L
6
)
(L
6
)
Table 1: Comparison of the Ψ and Φ functions.
distributed environment. As depicted in Figure 2, the total
number of query plans is more than four. However, we ig-
nore those plans that are unrealistic due to either large data
transmission over the network or expensive local/remote
computations. In the following sections, we only briefly
mention the unrealistic plans and the reasons we ignored
them.
4.1 TemporalFilterandSpatialSemi-join(T
F
S
J
)
With this method, depicted in Figure 2a, we join the helper
source, S
stations
, with S
schedules
. This is required to gen-
erate a common attribute (i.e., station coordinates) for the
further join operation with S
railroads
. However, the coordi-
nates of the stations are not exploited to improve the selec-
tivity of the temporal selection predicate.
As shown in Figure 2a, S
schedules
is first filtered and joined
with the helper source to generate intermediate results. Al-
ternative approaches can then be considered to join the in-
termediate results with S
railroads
. One approach is to per-
form σ
Q
S
on S
railroads
and transfer the results to the server
that holds S
schedules
. The advantage of this method is that
the result of σ
Q
S
usually constitutes a small set of data that
can be quickly transmitted over the network. On the other
hand, σ
Q
S
is an expensive operation rendering this method
impractical. We do not consider this method for our ex-
p eriments as its efficiency is always outperformed by other
metho ds.
The considered approach, termed T
F
S
J
, avoids expensive
complexity of σ
Q
S
by transferring the results of the tem-
p oral query to S
railroads
. The advantage of this method is
that we can perform a simpler spatial expression, σ
Q
0
S
, after
S
railroads
and intermediate results are joined. This reduces
the complexity of the query plan. However, due to the bad
selectivity of the temporal predicate (specially for longer
time intervals), large amount of data need to be transferred
over the network that may result in longer query processing
time. We consider this query plan in our experiments as
a comparison point. In Section 4.2, we describe a new ap-
proach which exploits the coordinates of the helper source
to improve the selectivity factor of the temporal predicate.
With this query execution plan, our query can be performed
in the following steps.
• Temporal Selection: First, we perform a selection on
the S
schedules
using the departure and arrival time and
the given time interval [t
a
, t
b
] to find all schedules that
are active during the given time interval. Next, we
join the selected schedules with S
stations
using station-
name to include coordinates of the stations in the se-
lected schedules.
• Spatial Semi-join: Next, we perform a spatial semi-
join between selected schedules and S
railroads
using
the coordinates of the stations and railroads.
• Spatial Filter : The results are then filtered using spa-
tial selection expression σ
Q
0
S
to select railroads that
intersect with the given point (x, y).
• Final Refinement: Finally, we calculate the estimated
time instant t at which each train reaches the given
p oint and exclude all trains for which t has no inter-
section with the interval [t
a
, t
b
].
The relational algebra expression for our query using the
T
F
S
J
query execution plan is:
σ
F R
(σ
Q
0
S
(σ
Q
T
(S
schedules
s
i
S
stations
)
<x
i
,y
i
>
S
railroads
))
(3)
4.2 Deviation Based Approach (DA)
We propose a different approach, termed Deviation Based
Approach, which is similar to T
F
S
J
except that it exploits
the coordinates of the stations to perform a spatio-temporal
selection predicate resulting in better selectivity. This ap-
proach reduces the number of the candidate schedules by
filtering out the schedules that correspond to the station
pairs connected through a path far from the query point
(x, y).
The core idea behind this approach is as follows. First, given
the coordinates of two stations, we can always compute the
shortest distance (straight line) between them. However, in
real-world, the railroad path between the two stations is not
a straight line. Hence, we estimate how much the real path
deviates from the straight line in the very worst case and de-
fine a term called Path Deviation to measure the deviation.
Extending the 2D area of this deviation with the time di-
mension, we obtain a 3D capsule shape object. Meanwhile,
the intermediate spatio-temporal tuples (station coordinates
joined with schedule time intervals) can be conceptualized
as straight lines in 3D space joining points ( x
i
, y
i
, t
a
) and
(x
j
, y
j
, t
b
). Consequently, the deviation filter only selects
those lines that intersect with the 3D capsule shape object.
This results in a much more effective filter as compared to
a pure temporal filter. Meanwhile, since this filter works on
the small set of point data (station coordinates) as opposed
to the large set of line data (railroad vectors), it is not as
computationally complex as the pure spatial filter.
Definition 4.1.: Path Deviation is defined as the ratio
of the sum of the euclidian distances between the start point
P
S
= (X
i
, Y
i
) and end point P
E
= (X
j
, Y
j
) with a given
point (x, y), over the euclidian distance between the start
and end points of a railroad segment.
P D(P
S
, P
E
, (x, y)) =
Distance(P
S
,(x,y))+(P
E
,(x,y))
Distance(P
S
,P
E
)
(4)
Figure 3: Graphical representation of the path de-
viation approach
Based on Definition 4.1, we can compute path deviation
for each schedule that is active during the given time in-
terval [t
a
, t
b
], and exclude all schedules that have path de-
viation greater than a pre-defined threshold. Path devia-
tion threshold, P
DT
, can be pre-determined or adaptively
computed during the query time. We present several algo-
rithms to compute the path deviation threshold and prove
that this approach does not result in any false drops (see
Section 4.2.1).
The difference between the execution plan for this approach
and the approach discussed in Section 4.1 is that the path
deviation selection predicate is applied to the results of the
temp oral selection b efore transmission to the server which
hosts S
railroads
.
Path deviation selection expression (σ
Q
DF
) for our query is
given below.
σ
Q
DF
= [P D(P
S
, P
E
, (x, y)) ≤ P
DT
] (5)
The graphical representation of this approach is shown in
Figure 3. Applying path deviation selection predicate is
similar to creating a capsule shaped object around the given
p oint (x, y). The length of the object depends on the given
time interval [t
a
, t
b
], while the width of the object depends
on the threshold. We select the schedules for which a straight
line between the starting and ending stations intersects with
the capsule shaped object.
The relational algebra expression of our query using this
query execution plan is:
σ
F R
(σ
Q
0
S
(σ
Q
DF
(σ
Q
T
(S
schedules
s
i
S
stations
))
<x
i
,y
i
>
S
railroads
)) (6)
Since the path deviation predicate provides a better selec-
tivity as compared to the temporal selection predicate, this
approach results in less data transfer between the servers
and better query response time.
4.2.1 Threshold Selection
In this section, we propose alternative algorithms to deter-
mine the threshold for the path deviation approach. Our
first method computes a constant value for the threshold.
We use Equation 7 to compute the threshold:
P
DT
= max(
length(railroad)
D istance(P
S
, P
E
)
) (7)
This equation computes the maximum ratio between the ac-
tual length of the railroad connecting all pairs of the starting
and ending points in S
railroads
and the euclidian distance
between them. We prove that this equation guarantees no
false drops, i.e., no candidate trains are excluded when using
this value for the path deviation threshold.
Theorem 4.2.: For Path Deviation Threshold P
DT
of
Equation 7, selection σ
Q
DF
results in no false drops.
Proof: We substitute P
DT
in Equation 5 with the value of
P
DT
computed by Equation 7.
σ
Q
DF
=
(Distance(P
S
, (x, y )) + Distance(P
E
, (x, y)))
(
D istance
(
P
S
, P
E
))
≤
max(length(railroad)
D istance(P
S
, P
E
))
(8)
(Distance(P
S
, (x, y ))+Distance(P
E
, (x, y))) is the length of
the shortest path, l
SE
, between the starting and ending points
that passes through the given point (x, y). Hence, if (x, y) is
on a railroad path linking the starting and ending points, the
length of the railroad must be greater then or equal to l
SE
,
which in turn implies that the Equation 8 is satisfied. This
means that none of the railroads that intersect with (x, y) are
excluded by the path deviation selection expression σ
Q
DF
.
The only disadvantage of a constant value for the threshold
is that a large value of the path deviation for some railroads
results in a large value of the overall threshold for the entire
network. For example, in real-world this scenario happens
if a railroad track is not a straight line between two stations
(shortest distance) due to some natural limitations (e.g., ex-
istence of a lake in the way). The larger the value of the
threshold, the worse the selectivity of the path deviation
selection predicate. This means that guaranteing no false
drops in path deviation approach (i.e., satisfying Equation
8) may result in selecting and transferring more schedules.
4.2.2 Adaptive Threshold
We propose two approaches to adaptively select the value of
the threshold.
1. With the first approach, we divide the spatial data
(e.g., S
railroads
) into distinct geographical regions and
calculate different threshold values for each region us-
ing Equation 6. In real-world, for a flat area such as a
desert, this would result in less conservative thresholds
while for an area with several mountains, a more con-
servative threshold will be chosen. Subsequently, dif-
ferent path deviation predicates with different thresh-
olds are applied to different regions. This results in
b etter selectivity for the path deviation selection pred-
icate as the high value of the threshold for a particular
region does not affect the regions with lower values of
the threshold.