The Seat Reservation Problem.
Joan Boyar and Kim S. Larsen.
Algorithmica, 25(4): 403-417, 1999.
We investigate the problem of giving seat reservations on-line. We assume that a train travels from a start station to an end station, stopping at k stations, including the first and last. Reservations can be made for any trip going from any station to any later station. The train has a fixed number of seats. The seat reservation system attempts to maximize income. We consider the case in which all tickets have the same price and the case in which the price of a ticket is proportional to the length of the trip. For both cases, we prove upper and lower bounds of Theta(1/k) on the competitive ratio of any "fair" deterministic algorithm. We also define the accommodating ratio which is similar to the competitive ratio except that the only sequences of requests allowed are sequences for which the optimal off-line algorithm could accommodate all requests. We prove upper and lower bounds of Theta(1) on the accommodating ratio of any "fair" deterministic algorithm, in the case in which all tickets have the same price, but Theta(1/k) in the case in which the ticket price is proportional to the length of the trip. The most surprising of these results is that all "fair" algorithms are at least 1/2-accommodating when all tickets have the same price. We prove similar results bounding the performance of any "fair" randomized algorithm against an adaptive on-line adversary. We also consider concrete algorithms; more specifically, First-Fit and Best-Fit.

Link to the publication at the publisher's site - subscription may be required.
Text required by the publisher (if any): The final publication is available at

open access (175 KB)
The same as the publisher's version, when the publisher permits. Otherwise, the author's last version before the publisher's copyright; this is often exactly the same, but sometimes fonts, page numbers, figure numbers, etc. are different. It may also be a full version. However, it is safe to read this version, and at the same time cite the official version, as long as references to concrete locations, numbered theorems, etc. inside the article are avoided.

other publications
Other publications by the author.