Exchanges for complex commodities toward a general purpose system
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Exchanges for Complex Commodities: Toward a General-Purpose System John Hershberger Committee: Eugene Fink Rafael Perez Dmitry B. Goldgof Combine the speed of the stock exchange with the flexibility of eBay + Motivation Build an automated

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Exchanges for Complex Commodities: Toward a General-Purpose System

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Exchanges for Complex Commodities:Toward a General-Purpose System

John Hershberger

Committee:

Eugene Fink

Rafael Perez

Dmitry B. Goldgof


  • Combine the speed of the stock exchange

with the flexibility of eBay

+

Motivation

  • Build an automated

  • exchange for trading

  • goods and services


Outline

  • Previous work


Outline

  • Previous work

  • One-attribute market


Outline

  • Previous work

  • One-attribute market

  • Multi-attribute market


Outline

  • Previous work

  • One-attribute market

  • Multi-attribute market

  • Large number of attributes


Outline

  • Previous work

  • One-attribute market

  • Multi-attribute market

  • Large number of attributes

  • Numeric attributes


Outline

  • Previous work

  • One-attribute market

  • Multi-attribute market

  • Large number of attributes

  • Numeric attributes

  • Complex orders


Outline

  • Previous work

  • One-attribute market

  • Multi-attribute market

  • Large number of attributes

  • Numeric attributes

  • Complex orders

  • Price functions


Outline

  • Previous work

  • One-attribute market

  • Multi-attribute market

  • Large number of attributes

  • Numeric attributes

  • Complex orders

  • Price functions

  • Main results


Combinatorial auctions

  • Complex commodities

  • Asymmetry between

  • buyers and sellers

  • Illiquid


Standardized exchanges

  • Simple commodities

  • Symmetry between

  • buyers and sellers

  • Liquid


$89.00

One-attribute market

Sell order

Price

Price

$89.02

Buy order

MCD

MCD

GE

IBM

GE

IBM

Stock symbol

Stock symbol


Sell order

$89.02

$89.00

One-attribute market

Price

Buy order

MCD

GE

IBM

Stock symbol


  • Table of all tradable items

  • For each item, a tree of prices

BA

GE

IBM

$88.94

MCD

PG

$88.93

$88.97

$88.96

$88.99

$88.92

$88.93

Table of items


50,000

30,000

Multi-attribute market

Mileage

Mileage

Sell order

Year

Year

03

03

02

02

01

01

00

00

Echo

Echo

Camry

Camry

Camaro

Camaro

Mustang

Mustang

Corvette

Corvette

Model

Model

Buyorder


Multi-attribute market

Mileage

50,000

30,000

Year

03

02

01

00

Echo

Camry

Camaro

Mustang

Corvette

Model


Model

Mustang

Camry

Corvette

Year

Year

Year

1996

1999

2000

1988

Mileage

Mileage

Mileage

Mileage

50K

10K

180K

20K

1996 Mustang,

50K miles,

$7,000

1999 Camry,

10K miles,

$18,000

2000 Camry,

180K miles,

$5,000

1988 Corvette,

20K miles,

$4,000

Retrieval tree

Retrieval tree (a.k.a. trie) of simple orders


Main structures

  • Trie of simple orders

  • List of complex orders


Model

Mustang

Camry

Corvette

Year

Year

Year

1996

1999

2000

1988

Mileage

Mileage

Mileage

Mileage

50K

10K

180K

20K

1996 Mustang,

50K miles,

$7,000

1999 Camry,

10K miles,

$18,000

2000 Camry,

180K miles,

$5,000

1988 Corvette,

20K miles,

$4,000

Best price

Depth-first search

Buy Order:Any car madeafter 1990


Model

Mustang

Camry

Corvette

Year

Year

Year

1996

1999

2000

1988

Mileage

Mileage

Mileage

Mileage

50K

10K

180K

20K

1996 Mustang,

50K miles,

$7,000

1999 Camry,

10K miles,

$18,000

2000 Camry,

180K miles,

$5,000

1988 Corvette,

20K miles,

$4,000

Best price among

found matches

Depth-first search With limited number of matches

Buy Order:Any car madeafter 1990

Limit: 2 matches

Actual best price


Model

Mustang

Camry

Corvette

Year

Year

Year

1999

2000

1988

1996

Mileage

Mileage

Mileage

Mileage

10K

180K

20K

50K

Cylinders

Cylinders

Cylinders

Cylinders

6

4

8

4

1996 Mustang

50K miles, 4 cyl.

1999 Camry

10K miles, 6 cyl.

1988 Corvette

20K miles, 8 cyl.

2000 Camry

180K miles, 4 cyl.

Large number of attributes


PATRICIA

Model

Camry

Year

Corvette,

1988,

20K,

8

Mustang,

1996,

50K,

4

1999,

10K,

6

2000,

180K,

4

1996 Mustang

50K miles, 4 cyl.

1999 Camry

10K miles, 6 cyl.

1988 Corvette

20K miles, 8 cyl.

2000 Camry

180K miles, 4 cyl.


50,000

30,000

Numeric attributes

Mileage

Mileage

Sell order

MPG

MPG

23

23

22

22

21

21

120

140

120

140

Top speed

Top speed

Buy order


50,000

Numeric attributes

Mileage

30,000

MPG

23

22

21

120

140

Top speed


PATRICIA with numeric attributes

PATRICIA gives high branching factor

Mileage

90K,

18,

100

30K,

28,

90

10K,

25,

140

100K,

20,

110

10K miles,

25 MPG,

140 m.p.h.

30K miles,

28 MPG,

90 m.p.h.

90K miles,

18 MPG,

100 m.p.h.

100K miles,

20 MPG,

110 m.p.h.


50

(50,45)

Car 1

Miles

MPG

40

Car 1

50K

45

(90,34)

Car 4

Car 2

20K

18

30

MPG

Car 3

70K

25

(20,18)

Car 2

(70,25)

Car 3

Car 4

90K

34

20

(30,16)

Car 5

Car 5

30K

16

Car 6

40K

10

10

(40,10)

Car 6

0

20K

40K

60K

80K

100K

Miles

KD-trees

Tree for handling numeric attributes


KD-trees

50

(50,45)

Car 1

40

Car 1

(90,34)

Car 4

30

MPG

(20,18)

Car 2

(70,25)

Car 3

20

(30,16)

Car 5

10

(40,10)

Car 6

0

20K

40K

60K

80K

100K

Miles


KD-trees

50

(50,45)

Car 1

40

Car 1

(90,34)

Car 4

30

MPG

Car 2

(20,18)

Car 2

(70,25)

Car 3

20

(30,16)

Car 5

10

(40,10)

Car 6

0

20K

40K

60K

80K

100K

Miles


KD-trees

50

(50,45)

Car 1

40

Car 1

(90,34)

Car 4

30

MPG

Car 3

Car 2

(20,18)

Car 2

(70,25)

Car 3

20

(30,16)

Car 5

10

(40,10)

Car 6

0

20K

40K

60K

80K

100K

Miles


KD-trees

50

(50,45)

Car 1

40

Car 1

(90,34)

Car 4

30

MPG

Car 3

Car 2

(20,18)

Car 2

(70,25)

Car 3

20

Car 4

(30,16)

Car 5

10

(40,10)

Car 6

0

20K

40K

60K

80K

100K

Miles


KD-trees

50

(50,45)

Car 1

40

Car 1

(90,34)

Car 4

30

MPG

Car 3

Car 2

(20,18)

Car 2

(70,25)

Car 3

20

Car 5

Car 4

(30,16)

Car 5

10

(40,10)

Car 6

0

20K

40K

60K

80K

100K

Miles


Car 1

Car 3

Car 2

Car 5

Car 4

Car 6

KD-trees

50

(50,45)

Car 1

40

(90,34)

Car 4

30

MPG

(20,18)

Car 2

(70,25)

Car 3

20

(30,16)

Car 5

10

(40,10)

Car 6

0

20K

40K

60K

80K

100K

Miles


KD-trees

50

(50,45)

Car 1

40

Car 1

(90,34)

Car 4

30

MPG

Car 3

Car 2

(20,18)

Car 2

(70,25)

Car 3

20

Car 5

Car 4

(30,16)

Car 5

Car 6

10

(40,10)

Car 6

0

20K

40K

60K

80K

100K

Miles


23

22

21

120

120

140

140

Top speed

Top speed

23

22

Buyorder

21

Complex orders

Mileage

Mileage

Sell order

50,000

50,000

MPG

MPG

25,000


120

140

Top speed

Complex orders

Mileage

50,000

MPG

25,000

23

22

21


Indexing of complex orders

Miles (K)

MPG

Car 1

40–60

40–50

Car 2

12–28

13–23

Car 3

52–88

20–30

Car 4

80–99

24–44

Car 5

25–35

11–21

Car 6

34–46

5–15


Indexing of complex orders

50

Car 1

40

Car 4

Car 1

Car 3

30

MPG

Car 3

Car 2

Car 2

20

Car 5

Car 4

Car 5

Car 6

10

Car 6

0

20K

40K

60K

80K

100K

Miles


Price functions

Price limit:

$32K – (2003 – Year) · $2K

$32K

Price

$30K

Year

$32K

03

$28K

Order:

2001-2003 Mustang

$30K

02

01

$28K

00

Camaro

Mustang

Corvette

Model


Price functions

Sell order

Mustang made in 2003

Price = $30,000

$32K

Price

$30K

Year

$32K

Buy order

2001-2003 Mustang

Price = $32K – (2003 – Year) · $2K

03

$28K

$30K

02

01

$28K

00

Camaro

Mustang

Corvette

Model


Price functions

  • Orders with identical attributes

  • are in the same leaf

  • Each leaf includes a tree of prices


Model

Mustang

Camry

Corvette

Year

Year

Year

1996

1999

2000

1988

Mileage

Mileage

Mileage

Mileage

50K

10K

60K

20K

1996 Mustang,

50K miles

1999 Camry,

10K miles

2000 Camry,

60K miles

1988 Corvette,

20K miles

$9K

$15K

$12K

$3K

$7K

$14K

$17K

$10K

Leaf nodes

Buy Order:Any car madeafter 1990


$9K

$15K

$12K

$3K

$7K

$14K

$17K

$10K

Leaf nodes

Buy Order:Any car madeafter 1990

Model

Mustang

Camry

Corvette

Year

Year

Year

1996

1999

2000

1988

Mileage

Mileage

Mileage

Mileage

50K

10K

60K

20K

1996 Mustang,

50K miles

1999 Camry,

10K miles

2000 Camry,

60K miles

1988 Corvette,

20K miles


$9K

$15K

$12K

$3K

$7K

$14K

$17K

$10K

Leaf nodes

Buy Order:Any car madeafter 1990

Model

Mustang

Camry

Corvette

Year

Year

Year

1996

1999

2000

1988

Mileage

Mileage

Mileage

Mileage

50K

10K

60K

20K

1996 Mustang,

50K miles

1999 Camry,

10K miles

2000 Camry,

60K miles

1988 Corvette,

20K miles


$9K

$15K

$12K

$3K

$7K

$14K

$17K

$10K

Leaf nodes

Buy Order:Any car madeafter 1990

Model

Mustang

Camry

Corvette

Year

Year

Year

1996

1999

2000

1988

Mileage

Mileage

Mileage

Mileage

50K

10K

60K

20K

1996 Mustang,

50K miles

1999 Camry,

10K miles

2000 Camry,

60K miles

1988 Corvette,

20K miles


$9K

$15K

$12K

$3K

$7K

$14K

$17K

$10K

Leaf nodes

Buy Order:Any car madeafter 1990

Model

Mustang

Camry

Corvette

Year

Year

Year

1996

1999

2000

1988

Mileage

Mileage

Mileage

Mileage

50K

10K

60K

20K

1996 Mustang,

50K miles

1999 Camry,

10K miles

2000 Camry,

60K miles

1988 Corvette,

20K miles


Leaf nodes

Buy Order:Any car madeafter 1990

Model

Mustang

Camry

Corvette

Year

Year

Year

1996

1999

2000

1988

Mileage

Mileage

Mileage

Mileage

50K

10K

60K

20K

1996 Mustang,

50K miles

1999 Camry,

10K miles

2000 Camry,

60K miles

1988 Corvette,

20K miles

$9K

$15K

$12K

$3K

Best

Match

$7K

$14K

$17K

$10K


Main results

  • Formalization of previous techniques

  • Identification of open problems

  • Theoretical solutions to some problems


Future work (Ph.D.)

  • Advanced indexing structures

  • Search for approximate matches

  • Trading different commodity

  • types in a common exchange


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