1 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 Ted Prepared by Raymond Chi-Wing Wong

Outline 1.Introduction 2.Problem Definition 3.Algorithm Spatial Approach 4.Discussion 5.Empirical Study 6.Related Work 7.Conclusion 2

1. Introduction HotelPrice ($) h1h1 100 h2h2 250 h3h3 200 h4h H = {h 1, h 2, h 3, h 4 } A = {a 1 } hotels attraction-site (e.g., Sea World) h4h4 a1a1 h2h2 h3h3 h1h1 Spatial LayoutPrice HotelDistance-to- SeaWorld (km) Price ($) h1h h2h h3h h4h Decision-Making Table According to the spatial layout and the price information, we can generate a decision table. Consider that a customer looks for a hotel near to Sea World 3

1. Introduction HotelPrice ($) h1h1 100 h2h2 250 h3h3 200 h4h H = {h 1, h 2, h 3, h 4 } A = {a 1 } hotels attraction-site (e.g., Sea World) h4h4 a1a1 h2h2 h3h3 h1h1 Spatial LayoutPrice HotelDistance-to- SeaWorld (km) Price ($) h1h h2h h3h h4h Decision-Making Table Consider that a customer looks for a hotel near to Sea World h 1 dominates h 3 (since h 1 is better than h 3 in terms of Distance-to- SeaWorld and Price).

1. Introduction HotelPrice ($) h1h1 100 h2h2 250 h3h3 200 h4h H = {h 1, h 2, h 3, h 4 } A = {a 1 } hotels attraction-site (e.g., Sea World) h4h4 a1a1 h2h2 h3h3 h1h1 Spatial LayoutPrice HotelDistance-to- SeaWorld (km) Price ($) h1h h2h h3h h4h Decision-Making Table Consider that a customer looks for a hotel near to Sea World h 2 does not dominate h 3 (since h 2 has a shorter Distance- to-SeaWorld than h 3 but h 2 has a higher price than h 3.)

1. Introduction HotelPrice ($) h1h1 100 h2h2 250 h3h3 200 h4h H = {h 1, h 2, h 3, h 4 } A = {a 1 } hotels attraction-site (e.g., Sea World) h4h4 a1a1 h2h2 h3h3 h1h1 Spatial LayoutPrice HotelDistance-to- SeaWorld (km) Price ($) h1h h2h h3h h4h Decision-Making Table Consider that a customer looks for a hotel near to Sea World Skyline: a set of hotels which are not dominated by other hotels Skyline = {h 1, h 2, h 4 } h 3 is dominated by h 1 A set of all “best” possible hotels

1. Introduction HotelPrice ($) h1h1 100 h2h2 250 h3h3 200 h4h H = {h 1, h 2, h 3, h 4 } A = {a 1 } hotels attraction-site (e.g., Sea World) h4h4 a1a1 h2h2 h3h3 h1h1 Spatial LayoutPrice HotelDistance-to- SeaWorld (km) Price ($) h1h h2h h3h h4h Decision-Making Table Consider that a new company wants to open a new hotel h f hfhf, h f } h f ? h f 2.0 ? How can we set the price of h f ?

1. Introduction HotelPrice ($) h1h1 100 h2h2 250 h3h3 200 h4h H = {h 1, h 2, h 3, h 4 } A = {a 1 } hotels attraction-site (e.g., Sea World) h4h4 a1a1 h2h2 h3h3 h1h1 Spatial LayoutPrice HotelDistance-to- SeaWorld (km) Price ($) h1h h2h h3h h4h Decision-Making Table Consider that a new company wants to open a new hotel h f hfhf, h f } h f ? h f 2.0 ?300 h f is dominated by h 2. $300 is not a competitive price.

1. Introduction HotelPrice ($) h1h1 100 h2h2 250 h3h3 200 h4h H = {h 1, h 2, h 3, h 4 } A = {a 1 } hotels attraction-site (e.g., Sea World) h4h4 a1a1 h2h2 h3h3 h1h1 Spatial LayoutPrice HotelDistance-to- SeaWorld (km) Price ($) h1h h2h h3h h4h Decision-Making Table Consider that a new company wants to open a new hotel h f hfhf, h f } h f ? h f 2.0 ?230 h f 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 h f, what greatest possible price can we set for h f such that h f is in the skyline?

1. Introduction HotelPrice ($) h1h1 100 h2h2 250 h3h3 200 h4h H = {h 1, h 2, h 3, h 4 } A = {a 1 } hotels attraction-site (e.g., Sea World) h4h4 a1a1 h2h2 h3h3 h1h1 Spatial LayoutPrice HotelDistance-to- SeaWorld (km) Price ($) h1h h2h h3h h4h Decision-Making Table Consider that a new company wants to open a new hotel h f hfhf, h f } h f ? h f 2.0 ?230 h f does not dominate any hotel. In order to make sure that h f is chosen by customers with a higher probability, we would like to set the price of h f such that 1. h f is in the skyline 2. h f dominates at least K hotels where K is a user parameter. Problem (Finding Simple Competitive Price): Given a set of existing hotels and a new hotel h f, what greatest possible price can we set for h f such that h f is in the skyline?

1. Introduction HotelPrice ($) h1h1 100 h2h2 250 h3h3 200 h4h H = {h 1, h 2, h 3, h 4 } A = {a 1 } hotels attraction-site (e.g., Sea World) h4h4 a1a1 h2h2 h3h3 h1h1 Spatial LayoutPrice HotelDistance-to- SeaWorld (km) Price ($) h1h h2h h3h h4h Decision-Making Table Consider that a new company wants to open a new hotel h f hfhf, h f } h f ? h f 2.0 ?230 h f dominates one hotel (i.e., h 4 ). In order to make sure that h f is chosen by customers with a higher probability, we would like to set the price of h f such that 1. h f is in the skyline 2. h f dominates at least K hotels where K is a user parameter. 210 $210 is a 1-dominating competitive price. Problem (Finding K-Dominating Competitive Price): Given a set of existing hotels, a new hotel h f and an integer K, what greatest possible price can we set for h f such that (1) h f is in the skyline and (2) h f dominates at least K hotels. Finding K-Dominating Competitive Price is more general than Finding Simple Competitive Price. Problem (Finding Simple Competitive Price): Given a set of existing hotels and a new hotel h f, what greatest possible price can we set for h f such that h f is in the skyline?

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 12

Outline 1.Introduction 2.Problem Definition 3.Algorithm Spatial Approach 4.Discussion 5.Empirical Study 6.Related Work 7.Conclusion 13

1. Introduction HotelPrice ($) h1h1 100 h2h2 250 h3h3 200 h4h H = {h 1, h 2, h 3, h 4 } A = {a 1 } hotels attraction-site (e.g., Sea World) h4h4 a1a1 h2h2 h3h3 h1h1 Spatial LayoutPrice HotelDistance-to- SeaWorld (km) Price ($) h1h h2h h3h h4h Decision-Making Table Consider that a new company wants to open a new hotel h f hfhf, h f } h f ? h f 2.0 ? A can contain more than one attraction-site {a 1, a 2, a 3 } a2a2 a3a3 Problem (Finding K-Dominating Competitive Price): Given a set of existing hotels, a new hotel h f and an integer K, what greatest possible price can we set for h f such that (1) h f is in the skyline and (2) h f dominates at least K hotels. Skyline requirement K-dominating requirement distance to a 1 … … … … distance to a 2 … … … … distance to a 3 … … … …

Outline 1.Introduction 2.Problem Definition 3.Algorithm Spatial Approach 4.Discussion 5.Empirical Study 6.Related Work 7.Conclusion 15

3. Algorithm Properties Algorithm 16

3. Algorithm Properties 2 properties for Skyline Requirement 1 property for K-dominating Requirement 17

3. Algorithm 2 Properties for Skyline Requirement Convex Hull Property Suppose that h f is in the convex hull of A. h f is in the skyline no matter what price we set for h f. 18 Spatial Layout hfhf h4h4 a1a1 h2h2 h3h3 h1h1 a2a2 a3a3 Convex hull

3. Algorithm 2 Properties for Skyline Requirement Non-Convex Hull Property Notations: I and U 19 Spatial Layout h4h4 a1a1 h2h2 h3h3 h1h1 a2a2 a3a3 hfhf I

3. Algorithm 2 Properties for Skyline Requirement Non-Convex Hull Property Notations: I and U 20 Spatial Layout h4h4 a1a1 h2h2 h3h3 h1h1 a2a2 a3a3 hfhf U

3. Algorithm 2 Properties for Skyline Requirement Non-Convex Hull Property Suppose that h f is in the convex hull of A. If we set the price to be min h ∈ I h.p, then h f is in the skyline 21 Spatial Layout h4h4 a1a1 h2h2 h3h3 h1h1 a2a2 a3a3 hfhf 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 22

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 h f dominates at least K hotels. 23 Spatial Layout h4h4 a1a1 h2h2 h3h3 h1h1 a2a2 a3a3 hfhf Suppose K = 2. We set the price of h f to be the 2 nd greatest price among these 3 hotels.

3. Algorithm Properties Algorithm 24

3. Algorithm find I and U find the convex hull of A (i.e., CH(A)) find the price (price sky ) based on 2 properties for the skyline requirement find the price (price dom ) based on 1 property for the K-dominating requirement price ← min{price sky, price dom } return price 25

3. Algorithm find I and U find the convex hull of A (i.e., CH(A)) find the price (price sky ) based on 2 properties for the skyline requirement find the price (price dom ) based on 1 property for the K-dominating requirement price ← min{price sky, price dom } return price 26 if h f is inside CH(A) then price sky ← ∞ else price sky ← min h ∈ I h.p price dom ← the K-th greatest price among all service-sites not in U

Outline 1.Introduction 2.Problem Definition 3.Algorithm Spatial Approach 4.Discussion 5.Empirical Study 6.Related Work 7.Conclusion 27

4. Discussion Handling Multiple Non-spatial Attributes How to set K 28

1. Introduction HotelPrice ($) h1h1 100 h2h2 250 h3h3 200 h4h H = {h 1, h 2, h 3, h 4 } A = {a 1 } hotels attraction-site (e.g., Sea World) h4h4 a1a1 h2h2 h3h3 h1h1 Spatial LayoutPrice HotelDistance-to- SeaWorld (km) Price ($) h1h h2h h3h h4h Decision-Making Table Consider that a new company wants to open a new hotel h f hfhf, h f } h f ? h f 2.0 ? A can contain more than one attraction-site {a 1, a 2, a 3 } a2a2 a3a3 Problem (Finding K-Dominating Competitive Price): Given a set of existing hotels, a new hotel h f and an integer K, what greatest possible price can we set for h f such that (1) h f is in the skyline and (2) h f dominates at least K hotels. distance to a 1 … … … … distance to a 2 … … … … distance to a 3 … … … … Each hotel can be incorporated with multiple non-spatial attributes.

4. Discussion Handling Multiple Non-spatial Attributes How to set K 30

4. Discussion How to set K Existing Models in Economic and Business Research Studying Customer Retention/Attrition (e.g., demand-and- supply model) 31

Outline 1.Introduction 2.Problem Definition 3.Algorithm Spatial Approach 4.Discussion 5.Empirical Study 6.Related Work 7.Conclusion 32

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 33

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. 34

5. Empirical Study Default Parameter K = 20 35

5. Empirical Study Measurements Price p max,s denotes price sky used in the algorithm p max,d denotes price dom used in the algorithm p max denotes the final price used in the algorithm Query Time 36

5. Empirical Study 37 Synthetic dataset

5. Empirical Study 38 Real dataset

Outline 1.Introduction 2.Problem Definition 3.Algorithm Spatial Approach 4.Discussion 5.Empirical Study 6.Related Work 7.Conclusion 39

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. 40

Outline 1.Introduction 2.Problem Definition 3.Algorithm Spatial Approach 4.Discussion 5.Empirical Study 6.Related Work 7.Conclusion 41

7. Conclusion Finding K-Dominating Competitive Price First one to study the problem Spatial Approach Experiments 42

Q&A 43

Backup Slides 44

5. Empirical Study 45 Synthetic dataset No. of attractions

5. Empirical Study 46 Synthetic dataset No. of hotels