1 Finding Competitive Price Yu Peng (Hong Kong University of Science and Technology) Raymond Chi-Wing Wong (Hong Kong University of Science and Technology)

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Finding Competitive Price

Yu Peng (Hong Kong University of Science and Technology)Raymond Chi-Wing Wong (Hong Kong University of Science and

Technology)

Presented by TedPrepared by Raymond Chi-Wing Wong

Outline1. Introduction2. Problem Definition3. Algorithm

Spatial Approach4. Discussion5. Empirical Study6. Related Work7. Conclusion

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1. Introduction

Hotel Price ($)

h1 100h2 250h3 200h4 220

3

H = {h1, h2, h3 , h4}A = {a1}

hotels

attraction-site (e.g., Sea World)

h4

a1

h2

h3 h

1

Spatial Layout Price

Hotel

Distance-to-SeaWorld (km)

Price ($)

h1 3.0 100h2 1.0 250h3 4.0 200h4 2.5 220

Decision-Making Table

According to the spatial layout and the price information, we can generate adecision table.

Consider that a customer looks for a hotel near to Sea World

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1. Introduction

Hotel Price ($)

h1 100h2 250h3 200h4 220

4

H = {h1, h2, h3 , h4}A = {a1}

hotels


h4

a1

h2

h3 h

1


Hotel


Price ($)

h1 3.0 100h2 1.0 250h3 4.0 200h4 2.5 220



h1 dominates h3 (since h1 is better than h3 in terms of Distance-to-SeaWorld and Price).

1. Introduction

Hotel Price ($)

h1 100h2 250h3 200h4 220

5

H = {h1, h2, h3 , h4}A = {a1}

hotels


h4

a1

h2

h3 h

1


Hotel


Price ($)

h1 3.0 100h2 1.0 250h3 4.0 200h4 2.5 220



h2 does not dominate h3 (since h2 has a shorter Distance-to-SeaWorld than h3 but h2 has a higher price than h3.)

1. Introduction

Hotel Price ($)

h1 100h2 250h3 200h4 220

6

H = {h1, h2, h3 , h4}A = {a1}

hotels


h4

a1

h2

h3 h

1


Hotel


Price ($)

h1 3.0 100h2 1.0 250h3 4.0 200h4 2.5 220



Skyline: a set of hotels which are not dominated by other hotels

Skyline = {h1, h2, h4}

h3 is dominated by h1

A set of all “best” possible hotels

1. Introduction

Hotel Price ($)

h1 100h2 250h3 200h4 220

7

H = {h1, h2, h3 , h4}A = {a1}

hotels


h4

a1

h2

h3 h

1


Hotel


Price ($)

h1 3.0 100h2 1.0 250h3 4.0 200h4 2.5 220


Consider that a new company wants to open a new hotel hf

hf

, hf}

hf ? hf 2.0 ?

How can we set the price of hf?

1. Introduction

Hotel Price ($)

h1 100h2 250h3 200h4 220

8

H = {h1, h2, h3 , h4}A = {a1}

hotels


h4

a1

h2

h3 h

1


Hotel


Price ($)

h1 3.0 100h2 1.0 250h3 4.0 200h4 2.5 220



hf

, hf}

hf ? hf 2.0 ?

300hf is dominated by h2.

$300 is not a competitive price.

1. Introduction

Hotel Price ($)

h1 100h2 250h3 200h4 220

9

H = {h1, h2, h3 , h4}A = {a1}

hotels


h4

a1

h2

h3 h

1


Hotel


Price ($)

h1 3.0 100h2 1.0 250h3 4.0 200h4 2.5 220



hf

, hf}

hf ? hf 2.0 ?

230hf is not dominated by any hotel.

$230 is a competitive price.

Problem (Finding Simple Competitive Price): Given a set of existing hotels and a new hotel hf, what greatest possible price can we set for hf such that hf is in the skyline?

1. Introduction

Hotel Price ($)

h1 100h2 250h3 200h4 220

10

H = {h1, h2, h3 , h4}A = {a1}

hotels


h4

a1

h2

h3 h

1


Hotel


Price ($)

h1 3.0 100h2 1.0 250h3 4.0 200h4 2.5 220



hf

, hf}

hf ? hf 2.0 ?

230hf does not dominate any hotel.

In order to make sure that hf is chosen by customers with a higher probability, we would like to set the price of hf such that1. hf is in the skyline2. hf dominates at least K hotels where K is a user parameter.


1. Introduction

Hotel Price ($)

h1 100h2 250h3 200h4 220

11

H = {h1, h2, h3 , h4}A = {a1}

hotels


h4

a1

h2

h3 h

1


Hotel


Price ($)

h1 3.0 100h2 1.0 250h3 4.0 200h4 2.5 220



hf

, hf}

hf ? hf 2.0 ?

230hf dominates one hotel (i.e., h4).

In order to make sure that hf is chosen by customers with a higher probability, we would like to set the price of hf such that1. hf is in the skyline2. hf dominates at least K hotels where K is a user parameter. 21

0$210 is a 1-dominating competitive price.

Problem (Finding K-Dominating Competitive Price): Given a set of existing hotels, a new hotel hf and an integer K,what greatest possible price can we set for hf such that (1) hf is in the skylineand (2) hf dominates at least K hotels.

Finding K-Dominating Competitive Price is more general than Finding Simple Competitive Price.


1. Introduction In this paper, we study the problem of

“finding K-dominating competitive price” Contributions:

First to study this problem Most existing studies focus on how to find hotels

in the skyline when the prices of the hotels are given.

Propose an algorithm based on spatial properties

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1. Introduction

Hotel Price ($)

h1 100h2 250h3 200h4 220

14

H = {h1, h2, h3 , h4}A = {a1}

hotels


h4

a1

h2

h3 h

1


Hotel


Price ($)

h1 3.0 100h2 1.0 250h3 4.0 200h4 2.5 220



hf

, hf}

hf ? hf 2.0 ?

A can contain more than one attraction-site{a1, a2, a3}

a2 a

3


Skyline requirementK-dominating requirement

distance to a1

…

…

…

…

…

distance to a2

…

…

…

…

…

distance to a3

…

…

…

…

…



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3. Algorithm Properties Algorithm

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3. Algorithm Properties

2 properties for Skyline Requirement 1 property for K-dominating

Requirement

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3. Algorithm 2 Properties for Skyline Requirement

Convex Hull Property Suppose that hf is in the convex hull of A.

hf is in the skyline no matter what price we set for hf.

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Spatial Layout

hf

h4

a1

h2

h3 h

1a2 a

3

Convex hull

3. Algorithm 2 Properties for Skyline

Requirement Non-Convex Hull Property

Notations: I and U

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Spatial Layout

h4

a1

h2

h3 h

1a2 a

3hf

I

3. Algorithm 2 Properties for Skyline

Requirement Non-Convex Hull Property

Notations: I and U

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Spatial Layout

h4

a1

h2

h3 h

1a2 a

3hf

U

3. Algorithm 2 Properties for Skyline Requirement

Non-Convex Hull Property Suppose that hf is in the convex hull of A. If we set the price to be minh∈I h.p, then hf is

in the skyline

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Spatial Layout

h4

a1

h2

h3 h

1a2 a

3hf

Suppose I contain some hotels. We set the smallest price among these hotels in I.

Otherwise, we can set any price.

3. Algorithm Properties

2 properties for Skyline Requirement 1 property for K-dominating

Requirement

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3. Algorithm 1 property for K-dominating

Requirement Suppose that there are at least K

service-sites not in U. If we set the price to be the K-th greatest price among all hotels not in U, then hf dominates at least K hotels.

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Spatial Layout

h4

a1

h2

h3 h

1a2 a

3hf

Suppose K = 2.

We set the price of hf to be the 2nd greatest price among these 3 hotels.

3. Algorithm Properties Algorithm

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3. Algorithm find I and U find the convex hull of A (i.e., CH(A)) find the price (pricesky) based on 2 properties for the

skyline requirement

find the price (pricedom) based on 1 property for the K-dominating requirement

price ← min{pricesky, pricedom} return price

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3. Algorithm find I and U find the convex hull of A (i.e., CH(A)) find the price (pricesky) based on 2 properties for the

skyline requirement

find the price (pricedom) based on 1 property for the K-dominating requirement

price ← min{pricesky, pricedom} return price

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if hf is inside CH(A) then pricesky ← ∞else pricesky ← minh∈I h.p

pricedom ← the K-th greatest price among all service-sites not in U



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4. Discussion Handling Multiple Non-spatial

Attributes How to set K

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1. Introduction

Hotel Price ($)

h1 100h2 250h3 200h4 220

29

H = {h1, h2, h3 , h4}A = {a1}

hotels


h4

a1

h2

h3 h

1


Hotel


Price ($)

h1 3.0 100h2 1.0 250h3 4.0 200h4 2.5 220



hf

, hf}

hf ? hf 2.0 ?

A can contain more than one attraction-site{a1, a2, a3}

a2 a

3


distance to a1

…

…

…

…

…

distance to a2

…

…

…

…

…

distance to a3

…

…

…

…

…

Each hotel can be incorporated with multiple non-spatial attributes.

4. Discussion Handling Multiple Non-spatial

Attributes How to set K

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4. Discussion How to set K

Existing Models in Economic and Business Research Studying Customer Retention/Attrition (e.g., demand-and-supply model)

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5. Empirical Study Dataset

Real Dataset Surf Hotel 20,000 hotels 4 attraction-sites

Synthetic Dataset Objects in North American (e.g., roads, populated

places and Cultural Landmarks) from Digital Chart of the World

200,000 hotels 20 attraction-sites

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5. Empirical Study Algorithms

Our Algorithm (3-Phase) Without Index With Index

Two Competitive Algorithms Blind

Try a set of possible prices in an increment count of 0.01 (i.e., 0.01, 0.02, 0.03, …)

For each possible price, test whether it satisfies the skyline requirement and the K-dominating requirement.

Pick the greatest price which satisfies the 2 requirements

Guided Similar to Blind But, try a set of possible prices of existing hotels.

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5. Empirical Study Default Parameter

K = 20

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5. Empirical Study Measurements

Price pmax,s denotes pricesky used in the algorithm pmax,d denotes pricedom used in the

algorithm pmax denotes the final price used in the

algorithm Query Time

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5. Empirical Study

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Synthetic dataset

5. Empirical Study

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Real dataset



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6. Related Work Skyline

One example is “spatial skyline” (VLDB06 and TODS09)

Price is given Application of Using Skyline

KDD08: Find Customer Preferences Based on Skylines VLDB09: Find a Set of Products which are in the Skyline

Most existing studies assume that an attribute value of a service-site is given. In this paper, we study how to find an attribute value, specifically price, of a new service-site.

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7. Conclusion Finding K-Dominating Competitive

Price First one to study the problem

Spatial Approach Experiments

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Q&A

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Backup Slides

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5. Empirical Study

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Synthetic dataset

No. of attractions

5. Empirical Study

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Synthetic dataset

No. of hotels

Documents

1 Finding Competitive Price Yu Peng (Hong Kong University of Science and Technology) Raymond Chi-Wing Wong (Hong Kong University of Science and Technology)