Introduction to firewall technology

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Foundations of Preferences in Database Systems
Author Werner Kie?ling Institute of
Computer Science University of Augsburg
Germany Presented by Haoyuan Wang
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Contents
Introduction
An Online Algorithm for Skyline Queries
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Introduction(Motivation)

• We Need the Real World
• If not perfect match, worse alternative
  acceptable.
• Requires best possible match making.
• Requires soft constraints.
• Preference-driven choice lagged behind

• We have the Exact World
• Delivering exact dream objects.
• Wishes satisfied completely or not at all.
• Uses hard constraints.
• Already investigated, such as SQL, E-R modeling,
  XML.

SELECT FROM car WHERE make 'Opel'
PREFERRING (category 'roadster' ELSE
category ltgt 'passenger' AND price AROUND
40000 AND HIGHEST(power)) CASCADE color
'red' CASCADE LOWEST(mileage)
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Introduction
Approaches to cope these two worlds

• Cooperative Database System
• Not comprehensive.

• Real world

• Exact world

• Preference Database Systems
• Intuitive semantics.
• Concise mathematical foundation.
• Constructive and extensible preference model.
• Conflicts of preferences do not cause system
  failure.
• Declarative preference query languages.

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Basics of Preferences

• What is preference ?
• Intuitively I like A better than B.
• Mathematically relation which is in strict
  partial order.
• irreflexive, transitive
• Our definition Preference P(A, ltP).
• A a set of attribute names.
• ltp ? dom(A) ? dom(A)
• a strict partial order referring to attribute
  names A.

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Basics of Preferences
Better-than graph G
Level 1 val1 val3
Level 2 val2 val4
Level 3 val5 val6 val7

• x ltP y, if y is a predecessor of x in G.
• Values in G without predecessor are maximal,
  being at level 1.
• x is on level j if the longest path from x to
  maxmal has j-1 edges.
• if no directed path between x and y, x and y are
  not ranked.

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Basics of Preferences
Special cases of preferences
Chain preference
Anti-Chain preference
Dual preference
Subset preference
Given P(A, P), every S?dom(A) induces a subset
reference P? (S, lt P? ), if for any x, y?S x P?
y iff xltP y.
If for all x, y?dom(A), x?y x ltP y ? y ltP x.
S? (S, ?), given any set of values S.
P?(A, P?) reverse the order on P, x ltP? y iff
yltP x.
All values are ranked in chain preference.
Any P can be completely reversely ranked
Any set, including dom(A) can be converted into
an anti-chain.
For any subset of A, ltP can apply.
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Preference Engineering Inductive Construction of
Preference-Nonnumerical base preference
POS preference POS(A, POS-set) P is a POS
preference, if x ltP y iff x ?POS-set ? y?POS-set
Intuitive definition A desired value should be
in a finite set of favorites POS?dom(A). If this
infeasible, better than getting nothing, any
other value from dom(A) is acceptable. Implication
all value in POS-set are
maximal, all value not in POS-set are at level 2
and worse than all POS-set values.
dom(A)
POS-set
Example POS(transmission, automatic)
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Preference Engineering Inductive Construction of
Preference-Nonnumerical base preference
NEG preference NEG(A, NEG-set) P is a NEG
preference, if x ltP y iff y ?NEG-set ? x?NEG-set
Intuitive definition A desired value should not
be in a finite set of dislikes NEG-set. If this
infeasible, better than getting nothing, any
other value from NEG-set is acceptable. Implicatio
n all value not in NEG-set
are maximal, all value in NEG-set are at level 2
and worse than all maximal values.
dom(A)
NEG-set
Example NEG(make, Ferrari)
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Preference Engineering Inductive Construction of
Preference-Nonnumerical base preference
POS/NEG preference POS/NEG(A, POS-set,
NEG-set) P is a POS preference, if x ltP y iff (
x ?NEG-set ? y ?NEG-set)?(x ?NEG-set ? x ?POS-set
? y?POS-set)
Intuitive definition A desired value should be
one in a finite set of favorites. Otherwise it
should not be any from a finite set of disjoint
dislikes. If this infeasible, better than getting
nothing, any other value from dislikes is
acceptable.
dom(A)
Example POS/NEG(color, yellow gray)
POS-set
NEG-set
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Preference Engineering Inductive Construction of
Preference-Nonnumerical base preference
POS/POS preference POS/POS(A, POS1-set,
POS2-set) x ltP y iff ( x ?POS2-set ? y ?
POS1-set)?(x ?POS1-set ? x ?POS2-set ?
y?POS2-set) ? (x ?POS1-set ? x ?POS2-set ?
y?POS1-set)
Intuitive definition A desired value should be
in a finite set of favorites POS1-set. Otherwise,
it should be from a disjoint finite set of
alternatives POS2-set. If this infeasible, better
than getting nothing, any other value is
acceptable.
Example POS/POS(category, cabrio roadster)
dom(A)
POS1-set
POS2-set
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Preference Engineering Inductive Construction of
Preference-Numerical base preference
AROUND preference AROUND(A, z) Given z ?dom(A),
for all v ?dom(A) . Define distance(v,z)
abs(v-z) P is called AROUND preference, if x
ltP y iff distance(x,z)gtdistance(y,z)
Intuitive definition The desired value should be
z. If this infeasible, values with shortest
distance from z are acceptable.
z
v
Example AROUND(price, 40000)
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Preference Engineering Inductive Construction of
Preference-Numerical base preference
BETWEEN preference BETWEEN(A,low, up) Given
zlow, up?dom(A)?dom(A), for all v ?dom(A) .
Define distance(v,low, up) if v ?low, up
then 0 else if v ltlow then low-v else v-up P is
called BETWEEN preference, if x ltP y iff
distance(x, low,up ) gt distance(y, low, up)
Intuitive definition The desired value should be
between the bounds of an interval. If this
infeasible, values with shortest distance from
the bounds are acceptable.
Example BETWEEN(mileage, 20000, 30000)
v
v
low
up
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Preference Engineering Inductive Construction of
Preference-Numerical base preference
LOWEST, HIGHEST preference LOWEST(A),
HIGHEST(A) P is called LOWEST preference, if x
ltP y iff x gt y P is called HIGHEST preference, if
x ltP y iff x lt y
Intuitive definition The desired value should be
as low (high) as possible.
Example LOW(price) HIGHEST(power)
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Preference Engineering Inductive Construction of
Preference-Numerical base preference
SCORE preference SCORE(A, f) P is called SCORE
preference, if for some x, y ?dom(A) x ltP y iff
f(x)ltf(y) Note ltp can be applied after the score
function f gives a value.
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Preference Engineering Inductive Construction of
Preference-Complex preference
Pareto preference P(A1?A2, ltP1? P2) Given
P1(A1, ltP1) and P2(A2, ltP2) and P2(A2, ltP2),
for x, y ?dom(A1)?dom(A2), define x lt P1? P2 y
iff (x1 ltP1 y1 ? (x2 ltp y2 ? x2y2)) ? (x2 ltP2
y2 ? (x1 ltP1 y1? x1y1))
Intuitive definition P1 and P2 are considered
as equally important preferences. In order for
x(x1, x2) to be better than y(y1, y2), it is
not tolerable that x is worse than y in any xi.
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Preference Engineering Inductive Construction of
Preference-Complex preference

• Pareto preference example
• For dom(A1)dom(A2)dom(A3)integer and
• P1 AROUND(A1, 0),
• P2 LOWEST(A2),
• P3 HIGHEST(A3),
• P4 (A1, A2, A3), ltP4) (P1?P2)?P3
• lets study a subset preference of P4 for the
  following set
• R(A1, A2, A3)val1(-5, 3, 4), val2(-5, 4, 4),
  val3(5, 1, 8), val4(5, 6, 6),
• val5(-6, 0, 6), val6(-6, 0, 4),
  val7(6, 2, 7)
• The better-than graph of P4 for subset R can be
  obtained by performing exhaustive better-than
  checks
• Level 1 val1 val3
  val5
• Level 2 val2 val4
  val7 val6

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Preference Engineering Inductive Construction of
Preference-Complex preference
Prioritized preference P(A1?A2, ltP1 P2) Given
P1(A1, ltP1) and P2(A2, ltP2) and P2(A2, ltP2),
for x, y ?dom(A1)?dom(A2), define x lt P1 P2 y
iff (x1 ltP1 y1 ? (x1y1 ? x2 ltP y2)

• Intuitive definition
• P2 is respected only when P1 does not mind.
• Example
• Lets revisit Example 1, now studying
• P8 (A1, A2, ltP8) P1P2
• R(A1, A2, A3)val1(-5, 3), val2(-5, 4),
  val3(5, 1), val4(5, 6), val5(-6, 0),
  val6(-6, 0), val7(6, 2)
• The better-than graph of P8 for subset R is
  this
• Level 1 val1 val3
• Level 2 val2 val4
• Level 3 val5 val6 val7

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Preference Engineering Inductive Construction of
Preference-Complex preference

Writing a preference query - a used-car scenario

1. Write wish-list
Julia wants to buy a used car for herself and her
friend Leslie, she wishes My favorite car is
Cabrio, but roadster is also good, I like an
automatic car and it should have a horsepower of
about 100, these issues are equally important to
me, but color is the most important, it should
not be gray, I do not care too much about price,
but since it is a used car, the lower, the
better. Julia goes to vendor Michael. Michael
wishes Clients wishes are always more
important than mine, I like to sell older cars,
the have higher commission . Julia also needs to
ask Leslie, Leslie wishes I agree with Julia,
I convinced Julia money should matter as much as
color, I like blue, if not available, please not
gray and red
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Preference Engineering Inductive Construction of
Preference-Complex preference
2. Convert wish-list to preference query terms
3. Use Pareto and Prioritization to add each
query terms
Julia P1POS/POS(category, cabrioroadster)
P2POS(transmission, automatic) P3AROUND(hors
epower, 100) P4LOWEST(price) P5NEG(color,
gray)
Q1(color, category, transmission,

horsepower,
price, ltQ1) P5((P1?P2?P3)P4)
Q2(color, category, transmission, horsepower,
price, year-of-construction, commission,ltQ2)
(Q1P6)P7((P5((P1?P2?P3)P4))P6)P7
Michael P6HIGHEST(year-of-construction) P7HIG
HEST(commission)
Q2(color, category, transmission, horsepower,
price, year-of-construction, commission,ltQ2)
(Q1P6)P7(((P5 ? P8 ? P4)(P1?P2?P3))P6))P7
Leslie P8POS/NEG(color, bluegray, red)
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Evaluation of Preference Queries Decomposition of
queries
How a preference query like the following is
evaluated Q2(color, category, transmission,
horsepower, price, year-of-construction,
commission,ltQ2) (Q1P6)P7(((P5 ? P8 ?
P4)(P1?P2?P3))P6))P7

• Decomposition of and ?
• ?P1P2(R) ?P1? ?P2 groupby A1(R)
• ?P1?P2(R) (?P1(R) ? ?P2 groupby A1(R)) ?
  (?P2(R) ? ?P1 groupby A2(R)) ? YY(P1P2, P2
  P1)R

• Decomposition of and ?
• ?P1P2(R) ?P1(R)? ?P2(R)
• ?P1?P2(R) ?P1(R)? ?P2(R)? YY(P1, P2)R

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Evaluation of Preference Queries BMO query model
Database preference PR Assume P(A, ltP), where
A(A1, A2, , Ak). a) Each RA ? dom(A) defines
a subset preference, called a database preference
and denoted by PR(RA, ltP) b) Tuple t?R is a
perfect match in a database set R, if tA
?max(P) ? tA ?R. Note preference query
performs a match-making between the stated
preference and the database preference. ?P(R)
t?R tA ?max(PR ) Note ?P(R) evaluates P
against database set R by retrievingall maximal
values from PR
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Shooting Stars in the Sky An Online Algorithm
for Skyline Queries Authors Donald Kossmann
Frank Ramsak Steen Rost Technische
Universit. at M. unchen Orleansstr. 34 81667
Munich Germany
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A Online Algorithm for Skyline Queries

• Contents
• Skyline Queries
• The NN Algorithm for 2-Dimensional Skylines
• An Example for 2-Dimensional Skylines
• The NN Algorithm for d-Dimensional Skylines

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Skyline Queries

• Retrieves all interesting points.
• Helps user get a big picture of interesting
  options.
• If users moves, skyline should be re-computed,
  users choice based on users location.

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The NN Algorithm for 2- Dimensional Skylines
Input Data set D Distance function f (Euclidean
distance) / Initialization the whole data space
needs to be inspected/ T (?, ?) / Loop
iterate until all regions have been
investigated/ WHILE (T ?0) Do (mx,
my)takeElement(T) IF(? boundedNNSearch(O, D,
(mx, my), f)) THEN ( nx, ny)
boundedNNSearch(O, D, (mx, my), f))
TT?(nx, my), (mx, ny) OUTPUT n ENDIF
ENDWHILE
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An Example for 2-Dimensional Skylines
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The NN Algorithm for d-Dimensional Skylines
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Approaches to Deal With Duplicates

• Laisser-faire
• propagate
• Merge
• Fine-grained Partitioning
• Hybrid Approaches

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Foundations of Preferences in Database Systems
Shooting Stars in the Sky An Online Algorithm
for Skyline Queries Authors Donald Kossmann
Frank Ramsak Steen Rost Technische
Universit. at M. unchen Orleansstr. 34 81667
Munich Germany