Computational Complexity of Air Travel Planning
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Computational Complexity of Air Travel Planning Carl de Marcken ITA Software [email protected] This document is an annotated set of slides on the computational complexity of air travel planning. The goal is to give somebody with an undergraduate level computer science background enough information to understand why air travel planning is an interesting and especially difficult problem. It provides a basic introduction to the air travel planning problem and then presents a variety of original computational complexity results as well as some related demos. The complexity slides assume a basic familiarity with formal languages, computational complexity and computability, but the introduction to the problem should be accessible without this. ITA Software produces search and optimization software for the travel industry. Our search engines power popular web sites such as Orbitz and Cheap Tickets; airline web sites such as America West, Continental Airlines and Alaska Airlines; computer reservation systems (CRS/GDSes) used by travel agencies, such as Galileo; and various travel agencies. ITA was founded by MIT computer scientists and is located adjacent to MIT in Cambridge, MA. Copyright 2003 ITA Software Notes for MIT course 6.034, Fall, 2003 1 Air Travel Planning QUERY SFOÆBOS April 2 BOSÆSFO April 5 Airline Agent Travel Agent Search Engine Travel Website Airline Website RESULT SFO AA123 BOS BOS AA191 DFW AA15 SFO $634 Flights Prices Seat availability Suppose a traveler is planning a round trip from San Francisco to Boston and back. Most likely they’ll contact an airline reservation agent or a travel agent, or perhaps visit an airline's website or a general travel website like Orbitz, providing a query made up of airport and travel time requirements. For the most part these agents are middlemen, and will pass the query off to one of a handful of companies, including ITA Software, that provide search engines for the airlines and the traveling public. Hopefully the search engine will return one or more answers to the query. Each answer consists of a specific set of flights for each part of the trip, and a price. The rest of this talk is about the difficulties search engines face answering such questions. The search engines run on databases of flights, prices, and seat availability, provided electronically over private networks by the 800 or so airlines of the world. The data is not directly available to the general public and access often must be negotiated with individual airlines. Flight data is updated daily or occasionally more frequently in the case of unexpected cancellations. Prices are updated about ten times a day, and seat availability continuously. A large portion of the flight, price and seat availability data, called published data, is used by all the major search engines, but a significant amount of private data is restricted. Copyright 2003 ITA Software Notes for MIT course 6.034, Fall, 2003 2 Outline • Introduction • Flights • How airline prices work • Complexity of travel planning • Demos • Seat availability • Further reading The talk starts by listing some fundamental properties of the flight network, but flights are simple relative to prices, and after the flight discussion will be a long but necessary introduction to airline prices. Then some basic computational complexity results about the difficulty of air travel planning are presented, with demos that illustrate the complexity results. The talk concludes with an introduction to seat availability processing, since it is an important part of understanding how airline prices work, though this information isn't used in the rest of the talk. 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This and most other data presented in this talk dates from 2001. Copyright 2003 ITA Software Notes for MIT course 6.034, Fall, 2003 4 The Flight Network • 4000 airports served by commercial airlines • Served by average of 4 airlines, connect to 8 others • Weighted by # of departures, 22 airlines, 64 destinations • Dominated by large airports – largest 1% (>4000 flights/day) have 40% of departures – largest 10% (>250 flights/day) have 85% of departures – reflects airlines’ hub-and-spoke system • Shortest path averages 3.5 in US, 5 worldwide (uniformly weighted) • Diameter > 20 • 30,000,000 scheduled commercial flights per year – 1 per second • 4000 – 10,000 planes in air, mostly large jets • 700,000 passengers in the air • 50% of flights within US and Canada There are more than 4000 airports served by commercial airlines worldwide.