author: werner kie ling institute of computer science university of augsburg

Author: Werner Kieling Institute of Computer Science University of Augsburg Germany

Presented by:Haoyuan Wang

Foundations of Preferences in Foundations of Preferences in Database SystemsDatabase Systems

An Online Algorithm for Skyline Queries

Basics of Preferences

Practical Work

Preference Engineering

Preference Algebra

Preference Queries

Introduction

Contents

Introduction(Motivation)

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.

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

SELECT * FROM car WHERE make = 'Opel' PREFERRING (category = 'roadster' ELSE

category <> 'passenger' AND price AROUND 40000 AND HIGHEST(power)) CASCADE color = 'red' CASCADE LOWEST(mileage);

Introduction

Exact world Real world

Cooperative Database System: Not comprehensive.

Approaches to cope these two worlds:

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.

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, <P). A: a set of attribute names. <p dom(A) dom(A) a strict partial order referring to attribute names A.

Basics of PreferencesBasics of Preferences

A={A1, A2, …, Ak} A={A1, A2, …, Ak}

<P

a b c d


Better-than graph G

x <P 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.

Level 1: val1 val3

Level 2: val2 val4

Level 3: val5 val6 val7


Special cases of preferences

Chain preference Anti-Chain preference Dual preference Subset preference

If for all x, y dom(A), x≠y: ∈

x <P y ∨ 　 y <P x.

S = (S, ), given any set of values S.

P=(A, P) reverse the order on P, x <P y iff y<P x.

Given P=(A, P), every Sdom(A) induces a subset reference P =(S, < P ), if for any x, yS: x P y iff x<P y.

All values are ranked in chain preference.

Any set, including dom(A) can be converted into an anti-chain.

Any P can be completely reversely ranked

For any subset of A, <P can apply.

Preference EngineeringPreference EngineeringInductive Construction of Preference-Nonnumerical base preference

POS preference: POS(A, POS-set)

P is a POS preference, if:

x <P y iff x POS-set yPOS-set

Intuitive definition:

A desired value should be in a finite set of favorites POSdom(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})


NEG preference: NEG(A, NEG-set)

P is a NEG preference, if:

x <P y iff y NEG-set xNEG-set


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.

Implication:

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})


POS/NEG preference:

POS/NEG(A, POS-set, NEG-set)

P is a POS preference, if:

x <P y iff ( x NEG-set y NEG-set)(x NEG-set x POS-set yPOS-set)


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) POS-setExample

POS/NEG(color, {yellow}; {gray})

NEG-set


POS/POS preference:

POS/POS(A, POS1-set, POS2-set)

x <P y iff ( x POS2-set y POS1-set)(x POS1-set x POS2-set yPOS2-set) (x POS1-set x POS2-set yPOS1-set)


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.

dom(A) POS1-set

Example

POS/POS(category, {cabrio}; {roadster})

POS2-set

Preference EngineeringPreference EngineeringInductive 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 <P y iff distance(x,z)>distance(y,z)


The desired value should be z. If this infeasible, values with shortest distance from z are acceptable.

Example

AROUND(price, 40000)

z v


BETWEEN preference: BETWEEN(A,[low, up])

Given z[low, up]dom(A)dom(A), for all v dom(A) .

Define distance(v,[low, up]) :=

if v [low, up] then 0 else

if v <low then low-v else v-up

P is called BETWEEN preference, if:

x <P y iff:

distance(x, [low,up] ) > distance(y, [low, up])


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

low up

v


LOWEST, HIGHEST preference:

LOWEST(A), HIGHEST(A)

P is called LOWEST preference, if

x <P y iff x > y

P is called HIGHEST preference, if

x <P y iff x < y


The desired value should be as low (high) as possible.

Example

LOW(price)

HIGHEST(power)


SCORE preference: SCORE(A, f)

P is called SCORE preference, if for some x, y dom(A):

x <P y iff f(x)<f(y)

Note: <p can be applied after the score function f gives a value.

Preference EngineeringPreference EngineeringInductive Construction of Preference-Complex preference

Pareto preference:

P=(A1A2, <P1 P2)

Given P1=(A1, <P1) and P2=(A2, <P2) and P2=(A2, <P2), for x, y dom(A1)dom(A2), define:

x < P1 P2 y iff

(x1 <P1 y1 (x2 <p y2 x2=y2))

(x2 <P2 y2 (x1 <P1 y1 x1=y1))


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.


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}), <P4) :=(P1P2)P3

let’s 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 2: val2 val4 val7 val6


Prioritized preference:

P=(A1A2, <P1& P2)

Given P1=(A1, <P1) and P2=(A2, <P2) and P2=(A2, <P2), for x, y dom(A1)dom(A2), define:

x < P1& P2 y iff

(x1 <P1 y1 (x1=y1 x2 <P y2)


P2 is respected only when P1 does not mind.

Example:Let’s revisit Example 1, now studying:P8 = ({A1, A2}, <P8) := P1&P2

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



Writing a preference query - a used-car scenario

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”

1. Write wish-list


3. Use Pareto and Prioritization to add each query terms

2. Convert wish-list to preference query terms

Julia:P1:=POS/POS(category, {cabrio};{roadster})P2:=POS(transmission, {automatic})P3:=AROUND(horsepower, 100)P4:=LOWEST(price)P5:=NEG(color, {gray})

Q1=({color, category, transmission, horsepower, price}, <Q1) :=P5&((P1P2P3)&P4)

Michael:P6:=HIGHEST(year-of-construction)

P7:=HIGHEST(commission)

Q2=({color, category, transmission, horsepower, price, year-of-construction, commission},<Q2) :=(Q1&P6)&P7=((P5&((P1P2P3)&P4))&P6)&P7

Leslie:P8:=POS/NEG(color, {blue};{gray, red})

Q2=({color, category, transmission, horsepower, price, year-of-construction, commission},<Q2) :=(Q1&P6)&P7=(((P5 P8 P4)&(P1P2P3))&P6))&P7

Evaluation of Preference Evaluation of Preference QueriesQueriesDecomposition of queries

Decomposition of ‘+’ and ‘’

[P1+P2](R)= [P1](R) [P2](R)

[P1P2](R)= [P1](R) [P2](R) YY(P1, P2)R

Decomposition of ‘&’ and ‘’

[P1&P2](R)= [P1] [P2 groupby A1](R)

[P1P2](R)= ([P1](R) [P2 groupby A1](R)) ([P2](R) [P1 groupby A2](R)) YY(P1&P2, P2& P1)R

How a preference query like the following is evaluated:

Q2=({color, category, transmission, horsepower, price, year-of-construction, commission},<Q2) :=(Q1&P6)&P7=(((P5 P8 P4)&(P1P2P3))&P6))&P7

Evaluation of Preference Evaluation of Preference QueriesQueriesBMO query modelDatabase preference PR

Assume P=(A, <P), where A=(A1, A2, …, Ak).

a) Each R[A] dom(A) defines a subset preference, called a database preference and denoted by:

PR=(R[A], <P)

b) Tuple tR is a perfect match in a database set R, if:

t[A] max(P) t[A] R.

Note: preference query performs a match-making between the stated preference and the database preference.

[P](R)={tR | t[A] max(PR )}Note: [P](R) evaluates P against database set R by retrievingall maximal values from PR

Shooting Stars in the Sky:An Online Algorithm for Skyline Queries

Authors:　 Donald　Kossmann　Frank　Ramsak　Steen　Rost

Technische　Universit.　at　M.　unchenOrleansstr.　3481667　MunichGermany

A Online Algorithm for Skyline QueriesA 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

Skyline Queries

Retrieves all interesting points.

Helps user get a big picture of interesting options.

If users moves, skyline should be re-computed, user’s choice based on user’s location.

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))

T=T{(nx, my), (mx, ny)}

OUTPUT n

ENDIF

ENDWHILE

An Example for 2-Dimensional Skylines

The NN Algorithm for d-Dimensional Skylines

Approaches to Deal With Duplicates

Laisser-faire

propagate

Merge

Fine-grained Partitioning

Hybrid Approaches

Shooting Stars in the Sky:An Online Algorithm for Skyline Queries

Authors:　 Donald　Kossmann　Frank　Ramsak　Steen　Rost

Technische　Universit.　at　M.　unchenOrleansstr.　3481667　MunichGermany

Foundations of Preferences in Foundations of Preferences in Database SystemsDatabase Systems

author: werner kie ling institute of computer science university of augsburg

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