1. Exchanges for Complex Commodities: Toward a General-Purpose System Committee: Eugene Fink Rafael Perez Dmitry B. Goldgof John Hershberger

2. Motivation Build an automated exchange for trading goods and services Combine the speed of the stock exchange with the flexibility of eBay +

3. Outline Previous work

4. One-attribute market Outline

5. Previous work One-attribute market Multi-attribute market Outline

6. Previous work One-attribute market Multi-attribute market Large number of attributes Outline

7. Previous work One-attribute market Multi-attribute market Large number of attributes Numeric attributes Outline

8. Previous work One-attribute market Multi-attribute market Large number of attributes Numeric attributes Complex orders Outline

9. Previous work One-attribute market Multi-attribute market Large number of attributes Numeric attributes Complex orders Price functions Outline

10. Previous work One-attribute market Multi-attribute market Large number of attributes Numeric attributes Complex orders Price functions Main results Outline

11. Combinatorial auctions Complex commodities Asymmetry between buyers and sellers Illiquid

12. Standardized exchanges Simple commodities Symmetry between buyers and sellers Liquid

13. One-attribute market Price Buy order Stock symbol $89.02 Price Sell order Stock symbol GEIBM MCD GEIBM MCD $89.00

14. One-attribute market Price Stock symbol GEIBM MCD $89.02 Buy order Sell order $89.00

15. Table of items Table of all tradable items BA GE IBM PG MCD $88.94 $88.93$88.97 $88.92$88.93 $88.96$88.99 For each item, a tree of prices

16. Multi-attribute market Mileage Buy order Model Year Mustang 50,000 00 03 Mileage Sell order Model Year 30,000 00 01 03 02 01 Echo Corvette Camaro Camry Echo Mustang Camry Camaro Corvette

17. Multi-attribute market Mileage Model Year Mustang 50,000 00 03 02 01 Echo Camry 30,000 Corvette Camaro

18. Retrieval tree Retrieval tree (a.k.a. trie) of simple orders Year 1999 Year 19961988 2000Camry Model CorvetteMustang Mileage 1999 Camry, 10K miles, $18,000 10K Mileage 50K 1996 Mustang, 50K miles, $7,000 Mileage 1988 Corvette, 20K miles, $4,000 20K Mileage 2000 Camry, 180K miles, $5,000 180K

19. Main structures Trie of simple orders List of complex orders

20. Depth-first search Model Mileage Year CorvetteMustang 1996 50K 1996 Mustang, 50K miles, $7,000 Year Camry 1999 Mileage 1999 Camry, 10K miles, $18,000 10K Mileage 1988 1988 Corvette, 20K miles, $4,000 20K Mileage 2000 2000 Camry, 180K miles, $5,000 180K Buy Order: Any car made after 1990 Best price

21. Depth-first search With limited number of matches Model Mileage Year CorvetteMustang 1996 50K 1996 Mustang, 50K miles, $7,000 Year Camry 1999 Mileage 1999 Camry, 10K miles, $18,000 10K Mileage 1988 1988 Corvette, 20K miles, $4,000 20K Mileage 2000 2000 Camry, 180K miles, $5,000 180K Buy Order: Any car made after 1990 Best price among found matches Actual best price Limit: 2 matches

22. Large number of attributes Model Corvette Year Camry 1999 Mileage 10K Mileage 2000 180K Cylinders 64 Mileage Year 1996 50K Cylinders 4 1996 Mustang 50K miles, 4 cyl. Year Mileage 1988 20K Cylinders 8 1988 Corvette 20K miles, 8 cyl. Mustang 1999 Camry 10K miles, 6 cyl. 2000 Camry 180K miles, 4 cyl.

23. PATRICIA Model Year Camry 1999, 10K, 6 2000, 180K, 4 1996 Mustang 50K miles, 4 cyl. 1988 Corvette 20K miles, 8 cyl. Mustang, 1996, 50K, 4 1999 Camry 10K miles, 6 cyl. 2000 Camry 180K miles, 4 cyl. Corvette, 1988, 20K, 8

24. Numeric attributes Mileage Top speed MPG 120140 50,000 23 22 21 Mileage Sell order Top speed MPG 30,000 Buy order 120140 23 22 21

25. Numeric attributes Mileage Top speed MPG 120140 50,000 23 22 21 30,000

26. PATRICIA with numeric attributes PATRICIA gives high branching factor Mileage 100K, 20, 110 10K miles, 25 MPG, 140 m.p.h. 100K miles, 20 MPG, 110 m.p.h. 10K, 25, 140 30K miles, 28 MPG, 90 m.p.h. 90K, 18, 100 90K miles, 18 MPG, 100 m.p.h. 30K, 28, 90

27. KD -trees Miles MPG Car 1 50K45 Car 3 70K25 Car 4 90K 34 Car 5 30K16 Car 6 40K10 Car 2 20K18 MPG 50 0100K20K40K60K80K 10 20 30 40 (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 Miles Tree for handling numeric attributes

28. MPG 50 10 20 30 40 (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 Car 1 20K40K60K80K Miles KD -trees 0100K

29. KD -trees MPG 50 10 20 30 40 (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 Car 1 Car 2 20K40K60K80K Miles 0100K

30. KD -trees MPG 50 10 20 30 40 (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 Car 1 Car 2 Car 3 20K40K60K80K Miles 0100K

31. KD -trees MPG 50 10 20 30 40 (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 Car 1 Car 2 Car 3 Car 4 20K40K60K80K Miles 0100K

32. KD -trees MPG 50 10 20 30 40 (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 Car 1 Car 5 Car 2 Car 3 Car 4 20K40K60K80K Miles 0100K

33. KD -trees Car 1 Car 5 Car 2 Car 3 Car 4 Car 6 MPG 50 10 20 30 40 (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 20K40K60K80K Miles 0100K

34. KD -trees MPG 50 10 20 30 40 (50,45) Car 1 (20,18) Car 2 (70,25) Car 3 (90,34) Car 4 (30,16) Car 5 (40,10) Car 6 Car 1 Car 5 Car 2 Car 3 Car 4 Car 6 20K40K60K80K Miles 0100K

35. Complex orders Mileage MPG Mileage MPG 50,000 Sell order 50,000 25,000 Buy order Top speed 120140 Top speed 120140 23 22 21 23 22 21

36. Complex orders MPG Mileage 50,000 25,000 Top speed 120140 23 22 21

37. Indexing of complex orders Miles (K) MPG Car 1 40–6040–50 Car 3 52–8820–30 Car 4 80–99 24–44 Car 5 25–3511–21 Car 6 34–465–15 Car 2 12–2813–23

38. Indexing of complex orders MPG 50 20K40K60K80K 10 20 30 40 Car 1 Car 2 Car 3 Car 4 Car 5 Car 6 Miles Car 1 Car 5 Car 2 Car 3 Car 4 Car 6 0100K

39. Price functions 01 02 03 00 Year Model Price CamaroMustangCorvette $32K $30K $28K $30K $32K Price limit: $32K – (2003 – Year) · $2K Order: 2001-2003 Mustang

40. Price functions 01 02 03 00 Year Model Price CamaroMustangCorvette $32K $30K $28K $30K $32K Sell order Mustang made in 2003 Price = $30,000 Buy order 2001-2003 Mustang Price = $32K – (2003 – Year) · $2K

41. Price functions Orders with identical attributes are in the same leaf Each leaf includes a tree of prices

42. Leaf nodes Model Mileage Year CorvetteMustang 1996 50K 1996 Mustang, 50K miles Year Camry 1999 Mileage 1999 Camry, 10K miles 10K Mileage 1988 1988 Corvette, 20K miles 20K Mileage 2000 2000 Camry, 60K miles 60K $3K $7K $9K $10K $12K $14K $15K $17K Buy Order: Any car made after 1990

43. Leaf nodes Model Mileage Year CorvetteMustang 1996 50K 1996 Mustang, 50K miles Year Camry 1999 Mileage 1999 Camry, 10K miles 10K Mileage 1988 1988 Corvette, 20K miles 20K Mileage 2000 2000 Camry, 60K miles 60K $3K $7K $9K $10K $12K $14K $15K $17K Buy Order: Any car made after 1990

44. Leaf nodes Model Mileage Year CorvetteMustang 1996 50K 1996 Mustang, 50K miles Year Camry 1999 Mileage 1999 Camry, 10K miles 10K Mileage 1988 1988 Corvette, 20K miles 20K Mileage 2000 2000 Camry, 60K miles 60K $3K $7K $9K $10K $12K $14K $15K $17K Buy Order: Any car made after 1990

45. Leaf nodes Model Mileage Year CorvetteMustang 1996 50K 1996 Mustang, 50K miles Year Camry 1999 Mileage 1999 Camry, 10K miles 10K Mileage 1988 1988 Corvette, 20K miles 20K Mileage 2000 2000 Camry, 60K miles 60K $3K $7K $9K $10K $12K $14K $15K $17K Buy Order: Any car made after 1990

46. Leaf nodes Model Mileage Year CorvetteMustang 1996 50K 1996 Mustang, 50K miles Year Camry 1999 Mileage 1999 Camry, 10K miles 10K Mileage 1988 1988 Corvette, 20K miles 20K Mileage 2000 2000 Camry, 60K miles 60K $3K $7K $9K $10K $12K $14K $15K $17K Buy Order: Any car made after 1990

47. Leaf nodes Model Mileage Year CorvetteMustang 1996 50K 1996 Mustang, 50K miles Year Camry 1999 Mileage 1999 Camry, 10K miles 10K Mileage 1988 1988 Corvette, 20K miles 20K Mileage 2000 2000 Camry, 60K miles 60K $3K $7K $9K $10K $12K $14K $15K $17K Buy Order: Any car made after 1990 Best Match

48. Main results Formalization of previous techniques Identification of open problems Theoretical solutions to some problems

49. Future work (Ph.D.) Advanced indexing structures Search for approximate matches Trading different commodity types in a common exchange