complex_pref: Complex preferences

Description

Complex preferences are used to compose different preferences orders. For example the Pareto composition (via operator *) is the usual operator to compose the preference for a Skyline query. The Skyline is also known as Pareto frontier. All complex preferences are mathematically strict partial orders (irreflexive and transitive).

Usage

## S3 method for class 'preference':
*(p1, p2)

## S3 method for class 'preference':
&(p1, p2)

## S3 method for class 'preference':
|(p1, p2)

## S3 method for class 'preference':
+(p1, p2)

reverse(p1)



empty()

Arguments

p1,p2

Preferences to be composed (either base preferences via base_pref or also complex preferences)

Skylines

The most important preference composition operator is the Pareto operator (p1 * p2) to formulate a Skyline query. A tuple t1 is better than t2 w.r.t. p1 * p2 if it is strictly better w.r.t. one of the preferences p1, p2 and is better or equal w.r.t. the other preference. The syntactical translation from other query languages supporting skylines/Preferences to rPref is as follows:

A query in the syntax from Borzsonyi et. al (2001) like "... SKYLINE OF a MAX, b MIN, c MAX" corresponds in rPref to the preferencehigh(a) * low(b) * high(c).
A query in the syntax from Kiessling (2002) like "... PREFERRING a LOWEST AND (b HIGHEST PRIOR TO c LOWEST)" corresponds in rPref tolow(a) * (high(b) & low(c)).
A query in the syntax of the "Skyline" feature of the commercial database "EXASOL EXASolution 5" like "... PREFERRING LOW a PLUS (b = 1 PRIOR TO LOW c))" corresponds in rPref tolow(a) * (true(b == 1) & low(c)).

Note that these query conversions can be done by show.query.

References

S. Borzsonyi, D. Kossmann, K. Stocker (2001): The Skyline Operator. In Data Engineering (ICDE '01), pages 421-430. W. Kiessling (2002): Foundations of Preferences in Database Systems. In Very Large Data Bases (VLDB '02), pages 311-322.

Examples

Run this code

# Define preference for cars with low consumption (high mpg-value)
# and simultanously high horsepower
p1 <- high(mpg) * high(hp)

# Perform the preference search
psel(mtcars, p1)