Evaluation of Expressions with Uncertainty in Databases

66 Pages·2013·0.45 MB·English

by  Moginraj Mohandas

University of New Orleans
ScholarWorks@UNO
University of New Orleans Theses and Dissertations Dissertations and Theses
5-18-2007
Evaluation of Expressions with Uncertainty in
Databases
Moginraj Mohandas
University of New Orleans
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Mohandas, Moginraj, "Evaluation of Expressions with Uncertainty in Databases" (2007).University of New Orleans Theses and
Dissertations.Paper 535.
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Evaluation of Expressions with Uncertainty in Databases
A Thesis
Submitted to the Graduate Faculty of the
University of New Orleans
in partial fulfillment of the
requirements for the degree of
Masters of Science
in
The Department of Computer Science
by
Moginraj Mohandas
B.Tech, Lal Bahadur Shastri College of Engineering, India, 2003
May, 2007
Copyright 2006, Moginraj Mohandas
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Acknowledgement
I wish to express my gratitude to a number of people who became involved with this
thesis, one way or another.
I am deeply indebted to my supervisor, Dr. Nauman Chaudhry whose help, stimulating
discussions; suggestions and encouragement helped me in all the time of research and for
writing of this thesis. In addition, I would like to thank Dr. Mahdi Abdelguerfi and Dr.
Golden Richard III for being on my thesis defense committee.
Finally, I would like to thank my family and friends for the continuous support and help
they provided to me. I would like to dedicate this thesis to my parents.
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Table of Contents
List of Tables.......................................................................................................................v
List of Figures…………………………………………………………………………….vi
Abstract…………………………………………………………………………………..vii
1 Introduction………………………………………………………………………..1
2 Expression Syntax and Terminology……………………………………………...5
2.1 Syntax of Crisp Expressions……...…………………………….....5
2.2 Syntax for Modeling Uncertainty in Expressions and Data
Items……………………................................................................9
3 Related Work…………………………………………………………………….14
3.1 Previous Work on Expressions: The Oracle Method…………….14
3.1.1 How Oracle stores Expressions………………….14
3.1.2 Evaluation of Expressions(EVALUATE
operator)………………………………………….15
3.1.3 Expression Data Type and Handling: Oracle
Approach………………………………………...16
3.2 Uncertainty Handling by different Systems……………………..17
3.2.1 Automated Ranking……………………………...17
3.2.2 Uncertainty in Publish/Subscribe Systems………21
3.2.3 Trio(ULDB)……………………………………..23
4 Semantics of Matching Uncertain Expressions and Uncertain
Data………………………...………………………………………………….....25
4.1 Evaluating Crisp Expressions against Crisp Data Items…………25
4.1.1 Semantics of Matching at the Predicate
Level……………………………….…………….25
4.1.2 Formal Model for Evaluating Crisp Expressions
against Crisp Data Items…………………………27
4.1.2.1Variable to describe Evaluation
cases……………………………...27
4.1.2.2Categorizing Cases of Crisp
Expression-Data Item Evaluation..28
4.2 Semantics of Matching Uncertain Predicates Against Uncertain
Data Terms……………………………………………………….29
4.3 Evaluation Semantics for Expressions and Data Items with
Approximate Matching and Uncertainty………………….……..38
4.3.1 Crisp Data Items, Crisp Expressions……..……...38
4.3.2 Uncertain Data Items, Uncertain Expressions…...42
5 Supporting Uncertain Expressions in a DBMS………………………………….46
5.1 Expression Data Type……………………………………………46
5.2 Details of Implementation……………………………………….46
6 Conclusion and Future Work………………………………………………….....51
References………………………………………………………………………………..53
Appendix.………………………………………………………………………………...55
Vita……………………………………………………………………………………….58
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List of Tables
Table 2.1 Example of an Expression Table…………………………………………….7, 8
Table 2.2 Example of a Conceptual Table with Data Items as column values……………9
Table 2.3 Example of Table with Expressions(with Uncertainty)…………………...11, 12
Table 3.1 Consumer Table…………………………………………………………...14, 15
Table 3.2 Example Table for ULDB……………………………………………………..24
Table 3.3 Example Table for ULDB……………………………………………………..24
Table 4.1 Example Table to show the various categorizing cases…………………...28, 29
Table 4.2 Comparison Table for Evaluation(without Uncertainty)………………….38, 39
Table 4.3 Comparison Table for Evaluation(with Uncertainty)……………………..42, 43
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List of Figures
Figure 5.1 Screenshot of Insert and Select in Postgresql……………………………….48
Figure 5.2 Screenshot of Evaluation of Expressions against Data Items using Evaluate
operator…………………………………………………………………………………50
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Abstract
Expressions are used in a range of applications like Publish/Subscribe, Ecommerce, etc.
Integrating support for expressions in a database management system (DBMS) provides
an efficient and scalable platform for applications that use Expressions. Support from
uncertain data and expressions can be beneficial but not currently provided for.
In this thesis, we investigate how expressions with uncertainty can be integrated in a
DBMS like other data. We describe the underlying theory and implementation of UNXS
(UNcertain eXpression System), a system that we have developed to handle uncertainty
in expressions and data. We develop a theoretical model to compare and contrast
different previous work in supporting uncertainty in DBMS and Publish/Subscribe
systems. We extend the existing approaches to propose new techniques for matching
uncertain expressions to uncertain data in UNXS. We then describe an implementation
that integrates this support in Postgresql DBMS, which to our knowledge is the first such
implementation.
.
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Chapter 1 Introduction
Expressions are a good way to model the interests of a user in expected data. Expressions
have been used in various application domains, such as, Publish/Subscribe [2, 13],
Ecommerce [11], Website Personalization [12], etc. In such application domains, users
want to specify their interest in expected data in terms of expressions defined on this data.
The application needs to persistently maintain these expressions and match data with
these expressions to inform users of items of their interest. For example, in a
Publish/Subscribe system [13, 2] for a “Real Estate” application, subscriptions
correspond to the interests of the user defined over various attributes of houses. These
subscriptions are matched against publications of houses being sold that are published by
an information provider.
Example:
Subscription: Notify me of houses with price less than forty thousand that have a garage
and have more than two bedrooms.
This subscription can formally be modeled as the following Expression:
price<40000 AND garage=yes AND bedrooms>2
This expression, as well as expressions defined by other users, would be matched with
Publications that are given by the Real Estate Agents, who are the information providers.
Many times users find it easier to express their interest in uncertain or vague terms, rather
than in precise terms [2], [9]. The need to process uncertain data [7] has also become very
prominent in database management system research, especially in recent years because of
the wide varieties of sources that data come from [13]. However, currently most database
management systems as well as publish/subscribe systems do not support uncertain data.
Such data models, that do not support uncertain data, are called crisp data models. But,
lets look at an example from the application “Real Estate”. A user may be certain that he
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can pay up to $40,000 for a house and the house must have more than 3 bedrooms.
Additionally, even though he would like to have the house to have a garden, but he is
willing to consider houses without a garden. Likewise, he would like the house to have a
garage, but gives greater priority to a garage than a garden. In case of publications too, a
Real Estate Agent might not be absolutely certain as to whether a particular house has a
garden. Such Uncertainties may occur because the information may not be available in its
entirety at a given point of time. This can happen in a variety of application domains as
the information may be gathered from multiple sources, some of which may have more
complete information than others. We can modify the previous example to illustrate the
need for modeling uncertainty.
Example:
Subscription : Notify me of houses with price less than forty thousand that have two
bedrooms. In addition, it would be good if these houses had a garage, even though it is
not a required criterion.
This subscription can be formally modeled via the following Expression that supports
Uncertainty:
price<40000 1.0 AND garage=yes 0.3 AND bedrooms>2 1.0
Notice that we have attached Confidence values with individual conditions in the
expression. The conditions on price and bedrooms have a Confidence value of 1.0 that
expresses the user’s requirement that any house of interest to them must meet these
conditions. The condition on garage has a Confidence of 0.3 and this means that meeting
this condition has less priority than the other conditions. Therefore, even if an Agent is
not completely certain whether a particular house has a garage, that house should be
considered for this subscription. However, matching Uncertain data with Uncertain
expressions requires that we have an appropriate theoretical model for determining the
match. We will develop such a theoretical model in this thesis.
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