Exchanges for Complex Commodities Search for Optimal Matches

Exchanges for Complex Commodities: Search for Optimal Matches Jianli Gong Committee: Eugene Fink Dmitry B. Goldgof Sudeep Sarkar

Motivation • Build an automated exchange for trading goods and services

Motivation • Build an automated exchange for trading goods and services • Combine the speed and liquidity of the stock exchange

Motivation • Build an automated exchange for trading goods and services • Combine the speed and liquidity of the stock exchange with the flexibility of e. Bay +

Outline • Previous work

Outline • Previous work • Complex exchange • Data structures

Outline • Previous work • Complex exchange • Data structures Josh, Jenny

Outline • Previous work • Complex exchange • Data structures • Optimal matches • Performance Josh, Jenny

Outline • Previous work • Complex exchange • Data structures • Optimal matches • Performance Josh, Jenny Jianli

Outline • Previous work • Complex exchange • Data structures • Optimal matches • Performance

Previous Work • Combinatorial auctions • Standardized exchanges

Combinatorial Auctions • Complex commodities • Asymmetry between buyers and sellers • Illiquid Examples: Opti. Bid, SBIDS, e. Mediator

Standardized Exchanges • Simple commodities • Symmetry between buyers and sellers • Liquid Examples: Stocks, Futures

Outline • Previous work • Complex exchange • Data structures • Optimal matches • Performance

Complex Exchange • Market • Orders • Fills

Market All items that can be traded form a market. Example: All conceivable vehicles compose a car market.

Orders An order is a subset of the market along with a price function.

Orders An order is a subset of the market along with a price function. Example: Any Mustang or Corvette.

Orders An order is a subset of the market along with a price function. Example: Any Mustang or Corvette; Mustang for $38, 000 or Corvette for $40, 000.

Orders An order is a subset of the market along with a price function. Example: Any Mustang or Corvette; Mustang for $38, 000 or Corvette for $40, 000, –$1 for every ten miles.

Buy and Sell Orders Price Buy order Sell order

Buy and Sell Orders Sell order Price Buy order

Fills Buy order: Any Color Sports Car $36, 000 Sell order: Silver Limo $50, 000 or Red Mustang $32, 000 Fill: Red Mustang $34, 000

Implemented Exchange Specific sell orders. Good: Sell a red Mustang, made in 1999. Bad: Sell any color Mustang, made before 1999.

Implemented Exchange Price Buy order Sell order

Implemented Exchange Sell order Price Buy order

Outline • Previous work • Complex exchange • Data structures • Optimal matches • Performance

Data Structures • Tree of sell orders • List of buy orders

Tree of Sell Orders Model Mustang Corvette

Tree of Sell Orders Model Mustang Year 1996 1997 Corvette Year 1985 1986 1988

Tree of Sell Orders Model Mustang Corvette Year 1996 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 1997 Mileage Year 1985 1986 Mileage 1988 Mileage

Tree of Sell Orders Model Mustang Year 1996 Mileage 50 K 1996 Mustang, 50 K miles, $5, 000 Corvette Camry Year 1997 Year 2000 Mileage 10 K Mileage 1999 180 K 1999 Camry, 10 K miles, $18, 000 1986 Mileage 2000 Camry, 180 K miles, $5, 000 1988 Mileage 20 K 1988 Corvette, 20 K miles, $4, 000

Trading Cycle Process all new orders Re-match all old orders No Stop trading? Yes

Processing Process Re-match Stop? For every new order: If it is a buy order, search for matches; if not filled, add it to the list. If it is a sell order, add it to the tree.

Re-Matching For every buy order: search for matches among the sell orders. Process Re-match Stop?

Outline • Previous work • Complex exchange • Data structures • Optimal matches • Performance

Optimal Matches The system searches for the best-price matches in the indexing structure.

Optimal Matches The system searches for the best-price matches in the indexing structure. • Depth-first search (Josh)

Optimal Matches The system searches for the best-price matches in the indexing structure. • Depth-first search (Josh) • Best-first search (Jianli)

Depth-First Search Model Mustang Year Corvette Camry Year 1996 1999 2000 1988 Mileage 50 K 180 K 20 K 1996 Mustang, 50 K miles, $7, 000 1999 Camry, 10 K miles, $18, 000 2000 Camry, 180 K miles, $5, 000 1988 Corvette, 20 K miles, $4, 000

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

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

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

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

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

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

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

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

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

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

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

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

Depth-First Search Main drawback: If there are many matching leaves, the search takes a long time.

Depth-First Search With Limited Number of Matches Model Mustang Year Corvette Camry Year 1996 1999 2000 1988 Mileage 50 K 180 K 20 K 1996 Mustang, 50 K miles, $7, 000 1999 Camry, 10 K miles, $18, 000 2000 Camry, 180 K miles, $5, 000 1988 Corvette, 20 K miles, $4, 000

Depth-First Search Buy Order: With Limited Number of Matches Any car made after 1990 Model Mustang Year Corvette Camry Year 1996 1999 2000 1988 Mileage 50 K 180 K 20 K 1996 Mustang, 50 K miles, $7, 000 1999 Camry, 10 K miles, $18, 000 2000 Camry, 180 K miles, $5, 000 1988 Corvette, 20 K miles, $4, 000

Depth-First Search Buy Order: With Limited Number of Matches Any car made after 1990 Model Mustang Year Corvette Camry Year Limit: 2 matches Year 1996 1999 2000 1988 Mileage 50 K 180 K 20 K 1996 Mustang, 50 K miles, $7, 000 1999 Camry, 10 K miles, $18, 000 2000 Camry, 180 K miles, $5, 000 1988 Corvette, 20 K miles, $4, 000

Depth-First Search Buy Order: With Limited Number of Matches Any car made after 1990 Model Mustang Year Corvette Camry Year Limit: 2 matches Year 1996 1999 2000 1988 Mileage 50 K 180 K 20 K 1996 Mustang, 50 K miles, $7, 000 1999 Camry, 10 K miles, $18, 000 2000 Camry, 180 K miles, $5, 000 1988 Corvette, 20 K miles, $4, 000

Depth-First Search Buy Order: With Limited Number of Matches Any car made after 1990 Model Mustang Year Camry Corvette Year Limit: 2 matches Year 1996 1999 2000 1988 Mileage 50 K 180 K 20 K 1996 Mustang, 50 K miles, $7, 000 1999 Camry, 10 K miles, $18, 000 2000 Camry, 180 K miles, $5, 000 1988 Corvette, 20 K miles, $4, 000

Depth-First Search Buy Order: With Limited Number of Matches Any car made after 1990 Model Mustang Year Camry Corvette Year Limit: 2 matches Year 1996 1999 2000 1988 Mileage 50 K 180 K 20 K 1996 Mustang, 50 K miles, $7, 000 Best price among found matches 1999 Camry, 10 K miles, $18, 000 2000 Camry, 180 K miles, $5, 000 1988 Corvette, 20 K miles, $4, 000

Depth-First Search Buy Order: With Limited Number of Matches Any car made after 1990 Model Mustang Year Camry Corvette Year Limit: 2 matches Year 1996 1999 2000 1988 Mileage 50 K 180 K 20 K 1996 Mustang, 50 K miles, $7, 000 Best price among found matches 1999 Camry, 10 K miles, $18, 000 2000 Camry, 180 K miles, $5, 000 Actual best price 1988 Corvette, 20 K miles, $4, 000

Depth-First Search With Limited Number of Matches Main drawback: The search may not find the best-price match.

Best-First Search • Store the best price for each subtree • Use these prices to guide the search

Best Prices for Subtrees Model Mustang Year Corvette Camry Year 1996 1999 2000 1988 Mileage 50 K 180 K 20 K 1996 Mustang, 50 K miles, $7, 000 1999 Camry, 10 K miles, $18, 000 2000 Camry, 180 K miles, $5, 000 1988 Corvette, 20 K miles, $4, 000

Best Prices for Subtrees Model Mustang Year 1996 $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 Camry Corvette Year 1999 $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Year 2000 1988 Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K 1988 Corvette, 20 K miles, $4, 000

Best Prices for Subtrees Model Mustang $7, 000 Year 1996 $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 Camry Year 1999 $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Corvette $5, 000 Year $4, 000 2000 1988 Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K 1988 Corvette, 20 K miles, $4, 000

Best Prices for Subtrees Model Mustang $7, 000 Year 1996 $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 $4, 000 Camry Year 1999 $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Corvette $5, 000 Year $4, 000 2000 1988 Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K 1988 Corvette, 20 K miles, $4, 000

Search for Best Price Model Mustang $7, 000 Year 1996 $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 1999 $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Any car made after 1990 $4, 000 Camry Year Buy Order: Corvette $5, 000 Year $4, 000 2000 1988 Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K 1988 Corvette, 20 K miles, $4, 000

Search for Best Price Model Mustang $7, 000 Year 1996 $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 1999 $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Any car made after 1990 $4, 000 Camry Year Buy Order: Corvette $5, 000 Year $4, 000 2000 1988 Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K 1988 Corvette, 20 K miles, $4, 000

Search for Best Price Model Mustang $7, 000 Year 1996 $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 1999 $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Any car made after 1990 $4, 000 Camry Year Buy Order: Corvette $5, 000 Year $4, 000 2000 1988 Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K 1988 Corvette, 20 K miles, $4, 000

Search for Best Price Model Mustang $7, 000 Year 1996 $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 1999 $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Any car made after 1990 $4, 000 Camry Year Buy Order: Corvette $5, 000 Year $4, 000 2000 1988 Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K 1988 Corvette, 20 K miles, $4, 000

Search for Best Price Model Mustang $7, 000 Year 1996 $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 1999 $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Any car made after 1990 $4, 000 Camry Year Buy Order: Corvette $5, 000 Year $4, 000 2000 1988 Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K 1988 Corvette, 20 K miles, $4, 000

Search for Best Price Model Mustang $7, 000 Year 1996 $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 1999 $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Any car made after 1990 $4, 000 Camry Year Buy Order: Corvette $5, 000 Year $4, 000 2000 1988 Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 Best price 20 K 1988 Corvette, 20 K miles, $4, 000

Quality Function A buyer can specify a quality function that ranks the matching sell orders.

Quality Function A buyer can specify a quality function that ranks the matching sell orders. The system searches for the matches with the highest quality.

Quality Function Example Quality of a car: +4 for each year after 1970

Quality Function Example Quality of a car: +4 for each year after 1970 – 5 for each 10 K miles

Quality Function Example Quality of a car: +4 for each year after 1970 – 5 for each 10 K miles – 6 for each $1, 000

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

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

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

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

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

Depth-First Search Buy Order: Any car made after 1990 Model Mustang Camry Year Corvette Year 1996 1999 2000 1988 Mileage 50 K 180 K 20 K 1996 Mustang, 50 K miles, $7, 000 1999 Camry, 10 K miles, $18, 000 2000 Camry, 180 K miles, $5, 000 Quality: 37 Quality: 3 Quality: 0 1988 Corvette, 20 K miles, $4, 000

Depth-First Search Buy Order: Any car made after 1990 Model Mustang Camry Year Corvette Year 1996 1999 2000 1988 Mileage 50 K 180 K 20 K 1996 Mustang, 50 K miles, $7, 000 1999 Camry, 10 K miles, $18, 000 2000 Camry, 180 K miles, $5, 000 Highest quality: 37 Quality: 3 Quality: 0 1988 Corvette, 20 K miles, $4, 000

Monotonic Attributes • The quality monotonically decreases with the price

Monotonic Attributes • The quality monotonically decreases with the price • Usually, it is also monotonic on several other attributes

Monotonic Attributes • The quality monotonically decreases with the price • Usually, it is also monotonic on several other attributes Car quality • Increases with the year • Decreases with the mileage

Best-First Search • For every subtree, store the best value of each monotonic attribute • Use these values to estimate the quality of the best match in every subtree

Best Values for Subtrees Model Mustang Year Corvette Camry Year 1996 1999 2000 1988 Mileage 50 K 180 K 20 K 1996 Mustang, 50 K miles, $7, 000 1999 Camry, 10 K miles, $18, 000 2000 Camry, 180 K miles, $5, 000 1988 Corvette, 20 K miles, $4, 000

Best Values for Subtrees Model Mustang Year 1996 50 K, $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 Corvette Camry Year 1999 10 K, $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Year 2000 1988 180 K, Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K, 20 K 1988 Corvette, 20 K miles, $4, 000

Best Values for Subtrees Model Mustang 1996, 50 K, $7, 000 Year 1996 50 K, $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 Corvette Camry Year 1999 10 K, $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 2000, 10 K, $5, 000 Year 1988, 20 K, $4, 000 2000 1988 180 K, Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K, 20 K 1988 Corvette, 20 K miles, $4, 000

Best Values for Subtrees Model Mustang 1996, 50 K, $7, 000 Year 1996 50 K, $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 2000, 10 K, $4, 000 Corvette Camry Year 1999 10 K, $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 2000, 10 K, $5, 000 Year 1988, 20 K, $4, 000 2000 1988 180 K, Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K, 20 K 1988 Corvette, 20 K miles, $4, 000

Search for Best Match Model Mustang 1996, 50 K, $7, 000 Year 1996 50 K, $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 1999 10 K, $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Any car made 2000, 10 K, $4, 000 after 1990 Corvette Camry Year Buy Order: 2000, 10 K, $5, 000 Year 1988, 20 K, $4, 000 2000 1988 180 K, Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K, 20 K 1988 Corvette, 20 K miles, $4, 000

Search for Best Match Model Mustang 1996, 50 K, $7, 000 Year 1996 50 K, $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 1999 10 K, $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Any car made after 1990 91 Corvette Camry Year Buy Order: 2000, 10 K, $5, 000 Year 1988, 20 K, $4, 000 2000 1988 180 K, Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K, 20 K 1988 Corvette, 20 K miles, $4, 000

Search for Best Match Model Mustang 1996, 50 K, $7, 000 Year 1996 50 K, $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 1999 10 K, $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Any car made after 1990 91 Camry Year Buy Order: Corvette 85 Year 1988, 20 K, $4, 000 2000 1988 180 K, Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K, 20 K 1988 Corvette, 20 K miles, $4, 000

Search for Best Match Model Mustang 1996, 50 K, $7, 000 Year 1996 50 K, $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 1999 10 K, $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Any car made after 1990 91 Camry Year Buy Order: Corvette 85 Year 38 2000 1988 180 K, Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K, 20 K 1988 Corvette, 20 K miles, $4, 000

Search for Best Match Model Mustang 37 Year 1996 50 K, $7, 000 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 1999 10 K, $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Any car made after 1990 91 Camry Year Buy Order: Corvette 85 Year 38 2000 1988 180 K, Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K, 20 K 1988 Corvette, 20 K miles, $4, 000

Search for Best Match Model Mustang 37 Year 1996 37 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 1999 10 K, $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Any car made after 1990 91 Camry Year Buy Order: Corvette 85 Year 38 2000 1988 180 K, Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K, 20 K 1988 Corvette, 20 K miles, $4, 000

Search for Best Match Model Mustang 37 Year 1996 37 Mileage 50 K 1996 Mustang, 50 K miles, $7, 000 Highest quality: 37 1999 10 K, $18, 000 Mileage 10 K 1999 Camry, 10 K miles, $18, 000 Any car made after 1990 91 Camry Year Buy Order: Corvette 85 Year 38 2000 1988 180 K, Mileage $5, 000 Mileage $4, 000 180 K 2000 Camry, 180 K miles, $5, 000 20 K, 20 K 1988 Corvette, 20 K miles, $4, 000

Outline • Previous work • Complex exchange • Data structures • Optimal matches • Performance

Performance Empirical evaluation: • 1, 500 MHz CPU • 1, 024 Mbyte memory • 166 MHz bus

Control Variables • Search strategy • Number of orders • Length of item description

Measurements • Processing time • Re-matching time • Throughput

Processing Time Re-match Stop? Logarithmic Scale Linear Scale 1, 000 time (sec) 400 10 300 200 0. 1 100 0. 001 1 10 100 1, 000 100, 000 number of orders 0 50 K 100 K 150 K 200 K 250 K number of orders Best-First Search, Unlimited DFS, and Limited DFS

Process Re-Matching Time Logarithmic Scale Re-match Stop? Linear Scale 1, 000 time (sec) 400 10 300 200 0. 1 100 0. 001 1 10 100 1, 000 100, 000 number of orders 0 50 K 100 K 150 K 200 K 250 K number of orders Best-First Search, Unlimited DFS, and Limited DFS

Process Total Time Re-match Stop? Logarithmic Scale Linear Scale 1, 000 time (sec) 400 10 300 200 0. 1 100 0. 001 1 10 100 1, 000 100, 000 number of orders 0 50 K 100 K 150 K 200 K 250 K number of orders Best-First Search, Unlimited DFS, and Limited DFS

Throughput Number of attributes 1 3 10 Orders per second 5, 800 1, 500 20

Throughput Number of attributes 1 3 10 Orders per second 5, 800 1, 500 20 orders per second 1, 000 10, 000 1 1 3 10 number of attributes Best-First Search, Unlimited DFS, and Limited DFS

Main Results • Use of quality functions • Search for optimal matches • Performance evaluation

Future Work • Extended sell orders • Advanced indexing structures, such as kd-trees and quadtrees • Search for approximate matches • Trading different commodity types in a common exchange