Preference Querieswith Aggregate Constraints

Markus Endres

University of Augsburg

Sion 2007

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Problem DescriptionTravel Preferences

Szenario: Vacation Planning - One week in Vienna

Preferences and wishes

Target:

Fulfill all preferences and keep a price ≤ 1050 e.

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Problem DescriptionAn Example

Flight Hotel CarQA, BC, 680 e Gran, 2*, 125 e VW, C, 120 eKLM, BC, 810 e Ritz, 4*, 250 e Audi, L, 175 eLH, FC, 990 e Expo, 3*, 360 e BMW, L, 210 e

Target:

Fulfill all preferences and keep a price ≤ 1050 e.

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Problem DescriptionAn Example

Flight Hotel CarQA, BC, 680 e Gran, 2*, 125 e VW, C, 120 eKLM, BC, 810 e Ritz, 4*, 250 e Audi, L, 175 eLH, FC, 990 e Expo, 3*, 360 e BMW, L, 210 e

Argh, very bad!

My preferences are fulfilled to the very best but the price of 1290 eexceeds my constraint of 1050 e.

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Problem DescriptionAn Example

Flight Hotel CarQA, BC, 680 e Gran, 2*, 125 e VW, C, 120 eKLM, BC, 810 e Ritz, 4*, 250 e Audi, L, 175 eLH, FC, 990 e Expo, 3*, 360 e BMW, L, 210 e

Yeah, fantastic!

The price of 1050 e exactly matches my budget and my preferences arealmost fulfilled.

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Big Question

How to retrieve allFlight - Hotel - RentalCarcombinations with best

possible completion of alluser preferencesin particular the

hard price constraint?

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The BruteForce Algorithm

Brute force

Compute cartesian product F × H × C

Determine all combinations with aggregate price ≤ 1050 e

Fulfill all user preferences best possible

Disadvantages

Damned time consuming

Unfeasible for E-Commerce

Empty result effect

Preferences maybe not satisfied

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Quality AssignmentAnd Further Algorithms

Useful but not feasible

Apply preference selection first

Problem: Empty result set

Quality assignment for preferences

perfect hit −→good hit −→bad hit −→

Flight Hotel CarQA, BC, 680 e, Gran, 2*, 125 e, VW, C, 120 e,KLM, BC, 810 e, Ritz, 4*, 250 e, Audi, L, 175 e,LH, FC, 990 e, Expo, 3*, 360 e, BMW, L, 210 e,

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Quality AssignmentAnd Further Algorithms

Useful but not feasible

Apply preference selection first

Problem: Empty result set

Quality assignment for preferences

perfect hit −→good hit −→bad hit −→

Flight Hotel CarQA, BC, 680 e, Gran, 2*, 125 e, VW, C, 120 e,KLM, BC, 810 e, Ritz, 4*, 250 e, Audi, L, 175 e,LH, FC, 990 e, Expo, 3*, 360 e, BMW, L, 210 e,

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Why Smilies?Makes this sense?

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The DOMINANCE AlgorithmAn Improvement

Dominance Criterion

Given items i and j such that

i .price ≥ j .price ∧ i .smiley < j .smiley

then there exists an optimal solution without item i .

Flight Hotel CarQA, BC, 680 e, Gran, 2*, 125 e, VW, C, 120 e,KLM, BC, 810 e, Ritz, 4*, 250 e, ///////Audi,////L,//////175/////e,////////LH,//////FC,//////990/////e,/// Expo, 3*, 360 e, /////////BMW,////L,//////210////e,////

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The DOMINANCE AlgorithmThe Algorithm

Assign preference qualities to items

Apply dominance criterion → much less items

Build all combinations with aggregate price ≤ 1050 e

Find best combinations concerning the user preferences

Flight Hotel CarQA, BC, 680 e, Gran, 2*, 125 e, VW, C, 120 e,KLM, BC, 810 e, Ritz, 4*, 250 e,

Expo, 3*, 360 e,

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The HEURISTICS AlgorithmAgain an Improvement

Good old sorting ...

Sorting by price after applying the dominance criterion sorts theundominated items by increasing smiley, too.

Flight Hotel CarQA, BC, 680 e, Gran, 2*, 125 e, VW, C, 120 e,KLM, BC, 810 e, Ritz, 4*, 250 e, ///////Audi,////L,//////175/////e,////////LH,//////FC,//////990/////e,/// Expo, 3*, 360 e, /////////BMW,////L,//////210////e,////

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The HEURISTICS AlgorithmThe Algorithm

Assign preference qualities to items

Apply dominance criterion → much less items

Build all combinations with aggregate price ≤ 1050 e

Sort undominated items by increasing price.

Guess a solution ≤ 1050 e

Find further / better preference solutions in a neighborhood

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The HEURISTICS AlgorithmThe Algorithm

Assign preference qualities to items

Apply dominance criterion → much less items

Build all combinations with aggregate price ≤ 1050 e

Sort undominated items by increasing price.

Guess a solution ≤ 1050 e

Find further / better preference solutions in a neighborhood

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The HEURISTICS AlgorithmAn Example

Flight Hotel CarBA, 180 e, Loyd, 65 e, Fiat, 99 e,FD, 380 e, Palm, 95 e, Opel, 105 e,QA, 680 e, Gran, 125 e, VW, 120 e, 925 eKLM, 810 e, Ritz, 250 e, Audi, 175 e,LH, 990 e, Expo, 360 e, BMW, 210 e,LH, 1090 e, Ritz, 460 e, Seat, 250 e,

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The HEURISTICS AlgorithmAn Example

Flight Hotel CarBA, 180 e, Loyd, 65 e, Fiat, 99 e,FD, 380 e, Palm, 95 e, Opel, 105 e,QA, 680 e, Gran, 125 e, VW, 120 e, 925 eKLM, 810 e, Ritz, 250 e, Audi, 175 e, 980 eLH, 990 e, Expo, 360 e, BMW, 210 e,LH, 1090 e, Ritz, 460 e, Seat, 250 e,

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The HEURISTICS AlgorithmAn Example

Flight Hotel CarBA, 180 e, Loyd, 65 e, Fiat, 99 e,FD, 380 e, Palm, 95 e, Opel, 105 e,QA, 680 e, Gran, 125 e, VW, 120 e, 1050 eKLM, 810 e, Ritz, 250 e, Audi, 175 e,LH, 990 e, Expo, 360 e, BMW, 210 e,LH, 1090 e, Ritz, 460 e, Seat, 250 e,

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Evaluation

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EvaluationPerformance Tests

3 relations

correlated data

up to 2000 items

random priceconstraint

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EvaluationNumber of Solutions

correct

maybeincomplete

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Summary and Outlook

Quality assignment →DOMINANCE & HEURISTICS

Performance enhancement

E-Commerce

Further aggregate constraints

Find other optimization techniques

Planning process

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Summary and Outlook

Quality assignment →DOMINANCE & HEURISTICS

Performance enhancement

E-Commerce

Further aggregate constraints

Find other optimization techniques

Planning process

Preference Queries with Aggregate Constraints Sion 2007 16 / 17

Questions???

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