Fly Cheaply: On the Minimum Fuel Consumption Problem

✍ Scribed by Timothy M. Chan; Alon Efrat

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 82 KB
• Volume: 41
• Category: Article
• ISSN: 0196-6774
• DOI: 10.1006/jagm.2001.1189

✦ Synopsis

In planning a flight, stops at intermediate airports are sometimes necessary to minimize fuel consumption, even if a direct flight is available. We investigate the problem of finding the cheapest path from one airport to another, given a set of n airports in 2 and a function l 2 × 2 → + representing the cost of a direct flight between any pair. Given a source airport s, the cheapest-path map is a subdivision of 2 where two points lie in the same region iff their cheapest paths from s use the same sequence of intermediate airports. We show a quadratic lower bound on the combinatorial complexity of this map for a class of cost functions. Nevertheless, we are able to obtain subquadratic algorithms to find the cheapest path from s to all other airports for any well-behaved cost function l: our general algorithm runs in O n 4/3+ε time, and a simpler, more practical variant runs in O n 3/2+ε time, while a special class of cost functions requires just O n log n time.