Download Database Support for Situational Awareness

1
Database Support
Awareness
for
Situational
Iosif Lazaridis, Sharad Mehrotra, Kriengkrai Porkaew and Robert
Winkler
Abstract. Providing database support for interactive 3D Visualization and
Situational Awareness (SA) is one of the keys to making such systems scale to
the complexity of real-world scenarios. It is desirable that SA systems be highly
realistic and intuitive to use. From a database perspective these requirements
translate into (i) support for large amount of heterogeneous spatio-temporal
data (to provide a convincing virtual environment, approximating the
complexity of reality), (ii) support for highly dynamic situations in which the
data may change frequently, (iii) support for mechanisms to deal with inherent
imprecision in the underlying information, and, (iv) powerful query interface
that allows users to pose varied and interesting queries that are answered with
minimum time delay. In this chapter, we outline emerging research results in the
field, especially in the context of the SATURN project, pointing to their direct
applicability to the Situational Awareness task. We describe techniques for the
representation of dynamic and mobile objects and their integration into a
database system by reviewing appropriate indexing and query processing
techniques. We also deal with spatial aggregate queries and present new
techniques to compute their answers in a time-critical environment.
1. Introduction
Modern 3D Visualization systems, especially for the task of Situational
Awareness (SA), pose novel challenges to their data management component.
As data incorporated in such systems increases both in volume and complexity,
data management emerges as one of the most important enabling factors for
their continued success. Typical Database Management Systems (DBMS) have
been designed for business-oriented applications (e.g., banking), thus they are
not immediately suited for the quite different task of Situational Awareness.
The main challenges for database systems for SA arise from the nature of data
typically stored in such systems. These potentially include all the types of
objects in the physical world. More specifically, for the simulation of military
operations, the objects to be stored in the database include spatial information
such as terrain and buildings, and spatio-temporal data such as moving objects
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(troops and vehicles), weather (wind, cloud cover, etc.) A broad classification of
these data could be as static data, i.e., data that remains unchanged with the
passage of time (e.g., terrain) and dynamic data, which conversely have a state
that can be given as a function of time.
Dynamic data can further be distinguished as stationary and mobile. In the first
case the location of the objects in question do not change with the passing of
time, but other properties do. An example would be a temperature sensor
deployed in the field; its position remains constant but the temperature reading
that it transmits to the system changes from moment to moment. Mobile objects
have the property that their spatial location changes with time. In a military
simulation application all land, sea and air vehicles are mobile objects.
Most data used in Situational Awareness applications differ from traditional data
stored in databases in that they frequently possess an inherent notion of relative
quality or precision. In a banking application that keeps track of account
balances this issue does not arise; there is a single number that gives us the
precise balance of an account. In the SA domain things are not that clear. There
exists a natural trade-off between the quality of the presentation (virtual
environment) and the computational cost that has to be paid to deliver this level
of quality. For instance, a geometric model of a mountain can be kept at various
levels of resolution that increasingly approximate the “real” mountain. The
visualization system can present a coarse approximation of the mountain at a
minimal computational cost but can provide a better approximation for
additional cost.
The notion of quality arises both in static data (like mountains) and in dynamic
data (e.g., aircraft). In static data it corresponds to the multiple resolution model
outlined in the previous paragraph. For dynamic data traditional database
systems follow the explicit update model. Under this model, whenever an object
in the world being modeled in the database changes the value of one of its
attributes, it issues a direct update of its representation in the database system.
E.g., every time a customer makes a withdrawal from his banking account, the
new balance is update in the database system. For highly dynamic systems
(including SA systems), this policy is not feasible. As an example, an aircraft
moves continuously through the air at every instance of time. To precisely
capture its motion we would have to issue updates at a very high rate. This is
undesirable, because the cost of supporting the high update rate will hinder
performance and most of these updates are never used (e.g., there is no reason to
update a temperature reading every second, if the user asks for the temperature
every day). Much work still needs to be done to support dynamic data without
an explicit update model. The work done so far has focused on storing an
attribute value periodically and estimating it using a prediction model for query
times in-between updates.
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We have outlined just a few of the challenges that database management for
Situational Awareness has to face. The entire data management component of
SA systems has to be designed with these considerations in mind. In this chapter
we focus on a variety of issues that arise in this domain. In particular we
summarize the work done in the SATURN project on the representation,
indexing and querying of mobile object databases and also the processing of
spatial aggregate queries for visualization.
2. Mobile Object Representation & Indexing
Mobile objects are objects in the virtual environment whose position (i) changes
continuously with time and (ii) is not reflected in the database by an explicit
update. Condition (ii) is important as we have mentioned, because of the
prohibitive cost of sustaining multiple frequent updates of objects. A mobile
object traces a trajectory through space-time. If we think of space-time as having
3 spatial and 1 temporal dimensions then each 4D point (x, y, z, t) can be used to
represent the position of an object at some particular time. Since the object is
mobile, this representation will change continuously with time. Thus, if we look
at the object in space-time, we will observe an arbitrary, continuous line each
point of which represents the object’s location at the particular instance of time.
Figure 1. Mobile Object Update Management Techniques
It is natural to index mobile objects using a multi-dimension index structure,
e.g., R-Tree [Guttman, 84]. Such a data structure clusters objects that are close
together in the indexed space (in our case 4D space-time). An R-Tree works by
grouping objects with bounding rectangles in a hierarchical manner. Each node
of the R-Tree contains all the bounding rectangles of its children. Queries
usually need to look only at a small region of the indexed space. Using an RTree they can avoid looking at regions that are disjoint from the query. Thus, an
R-Tree provides an efficient way to access multi-dimensional data.
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A significant problem in dynamic environments is that of update management,
i.e., how often and under which conditions the object’s representation in the
database should be changed to reflect its changing real-world parameters. In
[Wolfson, 98] the Adaptive Dead Reckoning technique (Figure 1.a) is proposed.
Between updates, the object’s location is estimated based on its previous
behavior. An update is issued when the discrepancy between the object’s actual
location and its estimated location exceeds a threshold value of uncertainty. This
threshold value should be set so as to minimize the update cost
(computational/communication cost) and the uncertainty cost (imprecision in
our query answering). Another technique, Disconnection Detecting Dead
Reckoning (Figure 1.b) decreases the uncertainty value as time passes. This
addresses the problem of objects not sending in their updates because they have
been disconnected from the network. As the uncertainty value decreases with
time, the probability that an update should be sent increases.
Figure 2. Parametric Vs Native Space Indexing
To effectively use an R-Tree to index mobile objects we need to define the
bounding rectangle that will be used to represent the object. This is defined as
[xmin, xmax] [ymin, ymax] [zmin, zmax] [tstart, tend] where [tstart, tend] is the interval of
time in which the object’s motion is valid and the other intervals bound the
object’s motion along the 3 spatial dimensions throughout the temporal interval.
An interesting problem that arises is that of segmenting the motion of objects
into more than one bounding rectangles. This increases the number of objects
stored in the database but also decreases the total volume occupied by these
objects. The analysis presented in [Porkaew, 00] indicates that this strategy is
advantageous if the dimensionality of the indexed space increases or the average
object size increases.
A different approach for indexing of mobile objects has been proposed in the
literature [Kollios, 99], [Saltenis, 00], [Porkaew, 00]. This parametric space
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indexing (PSI), as opposed to the previously described native space indexing
(NSI) uses a different set of parameters to represent an object. These could be
time, location and velocity. One of the problems of PSI is its sensitivity to the
parameters chosen. Query processing becomes troublesome if the indexed
motion contains acceleration. This is due to the fact that while in NSI both the
query and the objects are rectangles in the native space, in PSI a transformation
between native and parametric space has to be performed. Figure 2 illustrates
this problem by showing how spatio-temporal range queries are mapped onto a
parametric space.
A significant contribution of the work in [Porkaew, 00] is its classification of
possible queries that might be meaningful in a spatio-temporal application
context. Additionally, specific techniques for the efficient processing of such
queries both for NSI and PSI have been proposed and an empirical study
establishing the efficiency of the proposed methods was performed. Three main
classes of queries were studied:
(i) Spatio-Temporal Range Queries. The user specifies a range (interval) along
each spatial and along the single temporal dimension. The query returns all
objects that exist in the prescribed 3D spatial rectangle, during the specified
time. E.g., “all vehicles in the Nevada desert from 10a.m. to 2p.m.”
(ii) Spatial k-Nearest Neighbor (kNN) Queries. The user specifies a query point
P in 3D space and a time interval t. The k objects in the database that are
closest to P during t are returned. E.g., “five closest submarines to me in
the next 10 min.”
(iii) Temporal kNN Queries. The user specifies a time instance tq and a spatial
rectangle R. The k objects that are in R closest temporally to tq are returned.
E.g., “first four ambulances to the scene of the accident after it occurs”.
3. Dynamic Query for High Performance Visualization
One of the novel concepts in terms of a Situational Awareness system is that of
a Dynamic Query. In traditional database systems the query is issued explicitly,
the database evaluates it and returns the results. In a SA in which the user
himself moves through the virtual environment, it is often desirable to associate
a query with the user and to continuously evaluate it. An example of this would
be in a flight simulation application. One of the requirements of such an
application is to gather up and render all visible elements for each frame of the
simulation presentation. The information that needs to be retrieved from the
database depends on the user’s position in the virtual world and needs to be
refreshed as the position changes. This is the essence of a dynamic query: it is
associated with a mobile object and is continuously evaluated as the motion
parameters of that object change.
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As introduced in [Porkaew, 00] a dynamic query is a series of snapshot queries
Q1, Q2,…, Qn posed at successive times t1, t2,…, tn. The snapshot query could be
any typical spatio-temporal query, e.g., a range query (retrieve all objects that
exist in a given rectangle of space for a particular interval of time) or a kNearest Neighbor (kNN) query (retrieve the k objects in the database that are
closest to a query object).
Techniques to evaluate snapshot range and kNN queries are well studied in the
literature. Thus, a dynamic query can be evaluated by issuing a sequence of
snapshot queries and using standard techniques to retrieve their answers.
However this approach is unnecessary wasteful. The fundamental observation is
that in a typical dynamic query that arises in a visualization scenario, the
observer’s motion is continuous and thus for each two queries Qi, Qi+1 in the
dynamic query sequence that he issues the overlap of the results is likely to be
high. Thus, some part of the effort expended toward answering Qi can be re-used
to answer Qi+1 as well. The quality of the presentation can thus be preserved,
since lower delays in query answering correspond directly to a minimization of
the time required to build each individual frame to be displayed. Subsequently,
the efficient processing at the database level of the application enables high
frame-rate visualization with multiple visual elements.
Figure 3. I/O Performance of PDQ (left) and NPDQ (right)
We further differentiate between two types of dynamic queries: Predictive
Dynamic Queries (PDQ) and Non-Predictive Dynamic Queries (NPDQ). The
first type corresponds to the case that the sequence Qi is known beforehand. In
such a case all the objects that need to be retrieved are know a priori and thus
could –in principle– be pre-fetched into main memory. However this would
require a large memory buffer to be kept. Another problem would be that as the
indexed objects are mobile (hence imprecise), they might send an update that
makes them irrelevant to the query; thus they would have been wastefully prefetched. In our approach, the index structure (R-Tree) is traversed using a
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priority-based scheme. Nodes are sorted based on the time in which they will
first cross the query trajectory. Since the query is known in advance, we can also
maintain the time in which they will cross out of this trajectory. The application
iteratively reads objects from the priority queue based on their time of
appearance, making sure that all objects that should appear now are actually
fetched. A further cache mechanism in main memory sorts them based on their
disappearance time; thus the application clears the memory buffer from objects
as soon as they have crossed out of the query trajectory.
In the case of NPDQ the sequence Qi is not known exactly. However there is
still at least knowledge of the query posed at any given instance of time, Q as
well as the previous query in the sequence, P. These probably overlap to a great
degree unless the observer moves very fast or in a jerky, non-continuous
manner. Thus, the results of P can be utilized in answering Q. We will end up to
doing significantly less disk accesses to answer Q if we take care not to traverse
nodes of the index structure that are classified as discardable. If R is the
bounding rectangle of a node, it is easy to reason that the node is discardable iff
(QR)P. This means that if the part of a node that is contained in the current
query Q was also contained in P then that node has already been fetched and
thus we should avoid reading it again into main memory.
In Figure 3 we see the I/O performance of both PDQ and NPDQ as the
percentage of overlap between successive snapshots increases. The experiments
indicate a great increase in efficiency for PDQ even for very small percentage of
overlap. For NPDQ there is also a significant improvement that becomes more
pronounced as the overlap percentage increases.
4. Concurrency Control Mechanisms
In dynamic environments, the spatio-temporal information stored in the
databases might be frequently updated. Earlier, we had discussed the issue of
update management to reduce the overhead of updates. Another significant issue
that arises in dynamic environments is that of concurrent operations over the
database. Even though concurrency control in databases is a well studied
problem, in the application domains considered, data is accessed through
specialized access methods (e.g., multidimensional data structures such as Rtree). Concurrent access through such data structures has been surprisingly little
studied in previous literature and has been noted as one of the difficult open
research problems in [Gray, 93]. Concurrent access to data via a index structure
introduces two independent concurrency control (CC) problems:
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

Preserving consistency and integrity of the data structure in presence of
concurrent insertions, deletions and updates.
Protecting search regions from phantoms.
Below, we describe these problems and their solutions in more details in the
context of Generalized Search Trees (GiST) [Hellerstein, 95]. GiST is an index
structure that is extensible ``both'' in the data types it can index and in the
queries it can support. It is like a ``template'' – the application developer can
implement her own access method using GiST by simply registering a few
extension methods with the DBMS. In particular, the GiST template and be
instantiated by an R-tree and many other multidimensional access methods.
Developing CC techniques for GiST is particularly beneficial since it would
need writing the CC code only once and would allow concurrent access to the
database via any index structure implemented in the DBMS using GiST, thus
avoiding the need to write the code for each index structure separately.
We first discuss the consistency problem. Consider a GiST (configured as, say,
an R-tree) with a root node R and its two children nodes A and B. Concurrent
operations over the R-tree could result in the tree losing its integrity. To see this
consider two operations: an insertion of a new key k1 into B and a deletion of a
key k2 from B. Suppose the deletion operation examines R and discovers that k2,
if present, must be in B. Before it can examine B, the insertion operation causes
B to split into B and B' as a result of which k2 moves to B' (and subsequently
updates R). The delete operation now examines B and incorrectly concludes that
k2 does not exist. Many such similar situations that compromise data structure
intergrity could arise when operations execute concurrently. An approach to
avoid above execution and preserve the consistency of the multidimensional
data structures is studied in [Kornacker, 97].
We now move on to the problem of phantom protection. Consider a transaction
T1 reading a set of data items from a GiST that satisfy some search predicate Q.
Transaction T2 then inserts a data item that satisfies Q and commits. If T1 now
repeats its scan with the same search predicate Q, it gets a set of data items
(known as ``phantoms'') different from the first read. Phantoms must be
prevented to guarantee serializable execution.
Note that object level locking does not prevent phantoms since even if all
objects currently in the database that satisfy the search predicate are locked,
concurrent insertions1 into the search range cannot be prevented. There are two
1
These insertions may be a result of insertion of new objects, updates to existing objects
or rolling-back deletions made by other concurrent transactions.
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general strategies to solve the phantom problem, namely predicate locking and
its engineering approximation, granular locking.
In predicate locking,
transactions acquire locks on predicates rather than individual objects. Although
predicate locking is a complete solution to the phantom problem, it is usually
too costly. In contrast, in granular locking, the predicate space is divided into a
set of lockable resource granules. Transactions acquire locks on granules instead
of on predicates. The locking protocol guarantees that if two transactions request
conflicting mode locks on predicates p and p' such that p  p' is satisfiable, then
the two transactions will request conflicting locks on at least one granule in
common. Granular locks can be set and released as efficiently as object locks.
An example of the granular locking approach is the multi-granularity locking
protocol. Application of MGL to the key space associated with a B-tree is
referred to as key range locking (KRL).
Unfortunately, KRL cannot be applied for phantom protection in
multidimensional data structures since it relies on a total order of key values of
objects which does not exist for multidimensional data. Imposing an artificial
total order (say a Z-order) over multidimensional data to adapt KRL is not a
viable technique either. Instead, in [Chakrabarti, 98] we define the concept of a
lockable resource granules over the multidimensional key space. In order to
define the coverage of the granules, a granule predicate is associated with every
index node of a GiST. Let N be an index node and P be the parent of N. Let
BP(N) denote the bounding predicate of N. The granule predicate of N, denoted
by GP(N), is defined as BP(N) if N is the root and BP(N) GP(P) otherwise.
There is a lockable resource granule TG(N) (TG stands for tree granule)
associated with each index node N. The lock coverage of TG(N) is defined by
GP(N). The granules associated with the leaf nodes are called leaf granules
while those associated with the non-leaf nodes are called non-leaf granules.
Since the granules are based on the predicate space partitioning generated by the
GiST, they continuously adapt to the key distribution (by updating current
granules, creating new granules and destroying old ones) which is a key to the
effectiveness of this technique. Based on the above concept of lockable
granules, lock protocols for the various operations on GiSTs are developed. The
protocol developed is the first such granular locking solution to phantoms for
multidimensional access methods and represents a scalable and effective
approach to supporting concurrent operations over such data sets.
5. Fast Computation of Spatial Aggregate Queries
An important class of queries in database systems is that of aggregate queries.
Such queries look at a great amount of data and return an aggregate value on
them. In spatial applications like SA, aggregate queries are especially important
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since it is natural to want to discover some summary information about data
objects that are embedded in a particular region of space. Examples of this type
of spatial aggregate query are: “what is the number of armored vehicles within
20 miles of my position”, “what is the maximum wind velocity 50 miles ahead
in my flight path” and “what is the average concentration of enemy vehicles per
square mile in region X”.
Let us define a data space as Sn . The data items stored in the database are in
the form (loc, value) where loc  S, and val  D is the attribute value for the
object in location loc. For our purposes the data space is usually the physical 3D
space, hence S=3, and D is the domain of the attribute that we are measuring,
e.g., D=[0, fuelmax] is the domain of possible fuel levels in a vehicle. A spatial
aggregate query can now be formally defined as a pair (R, agg_type) where RS
is the query region and agg_type is the type of attribute we are interested in.
Usually but not necessarily agg_type is one of the Structured Query Language
(SQL) aggregates (MIN, MAX, COUNT, SUM, AVG). The answer of the query
is derived by gathering up all objects o such that o.loc  R and aggregating over
their values. An example of such a query would be (California, MAX) that
would return the maximum fuel level in any vehicle located in California.
Figure 4. Example of an MRA-Quadtree
It is apparent that since aggregate queries look at a large number of data items, it
is difficult to compute them under the time-restrictive demands imposed by an
interactive SA application. To address this problem, we have developed a
technique [Lazaridis, 00] that provides approximate answers at increasing
quality levels. The application can thus provide a desirable quality level together
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with the query and/or a deadline. Our technique either gives the best possible
answer before the specified deadline or stops when it is guaranteed that the
quality requirement has been reached. We define quality as follows: the
algorithm we propose returns and estimate of the query answer â and a range of
values I=[l, h]. This interval of uncertainty is such that the true answer to the
query aI. Quality is quantified by the length of I or |I| which is being reduced
during the run of the algorithm. Perfect quality is reached when I=[â, â].
The mechanism we have introduced, called a Multi-Resolution Aggregate Tree
(MRA-Tree) is hierarchical decomposition of data space S. Each node of the
MRA-Tree covers a region of S. The root covers the entire S. We store on each
node, along with the spatial decomposition information, aggregate information
(specifically MIN, MAX, SUM, COUNT values) about each of its children
nodes. An example of an MRA-quadtree can be seen in Figure 4.
A query can always be mapped to two sets of nodes in the MRA-tree, a set of
nodes that are completely contained in the query region (set NC) and a set of
nodes that are partially contained in the query region or are a superset of the
region (set NP). The contribution of nodes from set NC to the query is certain
and we do not need to visit their children. However, the contribution of nodes
from NP to the query is uncertain. Our algorithm specifies: (a) a technique to
estimate the value of the aggregate based on sets NC, NP, (b) a technique to
provide minimum 100% intervals of confidence I as we have described above
and (c) a method for choosing nodes from NP to explore by visiting their
children.
We will briefly outline the above for COUNT queries, a description for all SQLtype aggregates can be found in [Lazaridis, 00]. It is obvious that given a query
region R and sets of nodes NC, NP the count of data items in the query must be
in the interval:


I count  
count N ,
count N 
count N 
 NNC

N NC
N NP



To estimate the answer of the query, given NC, NP we assume that data items
are uniformly distributed in partially overlapping nodes. If pN is the fraction of
node N in the query region then our estimate is:
E (count R ) 
 count
N NC
N

p
N NP
N
count N
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An optimal traversal policy would aim to maximally reduce the uncertainty
interval for a given number of nodes. Such a policy is impossible to be derived
since we cannot know a priori how much a particular node will decrease the
uncertainty. A heuristic that can be used is based on each node’s contribution to
the uncertainty interval. It is easy to see that for the COUNT example, the
contribution of some node N is equal to its count, i.e., countN. Thus a simple but
effective traversal policy would keep partially overlapping nodes in a priority
queue keyed on count and traverse them in order of increasing count.
Figure 5. Error Decrease as MRA-tree nodes are visited (left) and MRA-tree
comparision with plain quadtree index scan (right)
The experimental results both in synthetic and real-life spatial data indicate that
this technique can be used very effectively to provide approximate aggregate
answers. Even for exact answering it has been shown that the results are quite
good; this is because in the course of the algorithm we don’t need to visit the
subtree rooted in nodes of set NC, saving a lot of computational cost. In Figure 5
we see the method’s performance on an MRA-quadtree using synthetic data.
Both in terms of nodes visited for an exact answer (as compared to a normal
quadtree index scan) and in the decrease of error of estimation, the technique is
shown to be highly effective.
6. Summary,
Conclusions
Recommendations
(Lessons
Learned),
and
We have described a variety of significant challenges that arise in the context of
large-scale Situational Awareness applications. The volume of data in such
applications today has already reached the point where efficient database
management becomes one of the most critical factors for their success. In the
future, as the desire for richer, more highly interactive and meaningful virtual
environments becomes more pronounced, it will be impossible to build such
systems if their database component is not given its proper attention.
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The most important lesson emerging from our experience with SA systems is
how instrumental the notion of quality is to their success. A precise definition of
quality is often elusive, but its absence is felt strongly by the users of this type of
systems. From the database perspective, quality can be viewed as consisting of
two factors: (i) allowing the user to pose novel, interesting queries that highly
interactive applications require, and (ii) providing the best possible answer to the
user’s queries in an environment with strict timing constraints.
Our work in the SATURN project as outlined in this chapter addresses some of
these issues. We have proposed new ways to represent spatio-temporal
information in the database system, new query types that can be supported at the
database level itself and efficient processing techniques to produce answers at a
guaranteed level of quality. Much more needs to be done toward the goal of a
truly quality cognizant database system. Such a system will integrate a plethora
of new data management technologies for fast and reliable access to dynamic,
imprecise data. This new added functionality of the database system will enable
a host of exciting new applications that have hitherto been impossible.
References
[Chakrabarti, 98]
K. Chakrabarti and S. Mehrotra, “Dynamic Granular
Locking Approach to Phantom Protection in RTrees”, February 1998, IEEE ICDE Conference.
[Chakrabarti, 99]
K. Chakrabarti and S. Mehrotra, “Efficient
Concurrency Control in Multidimensional Access
Methods”, June 1999, ACM SIGMOD Conference.
[Gray, 93]
J. Gray and A. Reuter, “Transaction Processing:
Concepts and Techniques”, 1993, ISBN 1-55860190-2
[Guttman, 84]
A. Guttman, “R-Trees: A Dynamic Index Structure
for Spatial Searching”, June 1984, ACM SIGMOD
Conference.
[Hellerstein, 95]
J. Hellerstein, J. Naughton and A. Pfeffer,
“Generalized Search Trees for Database Systems”,
September 1995, VLDB Conference.
14
[Kollios, 99]
G. Kollios, D. Gunopoulos and V. Tsotras, “On
Indexing Mobile Objects”, June 1999, ACM PODS
Symposium.
[Kornacker, 97]
M. Kornacker, C. Mohan and J. Hellerstein,
“Concurrency and Recovery in Generalized Search
Trees”, June 1997, ACM SIGMOD Conference.
[Lazaridis, 00]
I. Lazaridis and S. Mehrotra, “Progressive
Approximate Aggregate Queries with a MultiResolution Tree Structure”, August 2000. Submitted
for publication.
[Porkaew, 00]
K. Porkaew, “Database Support for Similarity
Retrieval and Querying Mobile Objects”, Ph.D.
thesis, Department of Computer Science, University
of Illinois at Urbana-Champaign, 2000.
[Saltenis, 00]
S. Saltenis, C. Jensen, S. Leutenegger, M. Lopez,
“Indexing the Positions of Continuously Moving
Objects”, May 2000, ACM SIGMOD Conference.
[Wolfson, 98]
O. Wolfson, B. Xu, S. Chamberlain, L. Jiang,
“Moving Objects Databases: Issues and Solutions”,
July 1998, IEEE SSDBM Conference.