The relative worst order ratio applied to seat reservation

Abstract

The relative worst order ratio is a new measure for the quality of online algorithms, which has been giving new separations and even new algorithms for a variety of problems. Here, we apply the relative worst order ratio to the seat reservation problem, the problem of assigning seats to passengers in a train. For the unit price problem, where all tickets have the same cost, we show that First-Fit and Best-Fit are better than Worst-Fit, even though they have not been separated using the competitive ratio. The same relative worst order ratio result holds for the proportional price problem, where the ticket price is proportional to the distance travelled. In contrast, no deterministic algorithm has a competitive ratio, or even a competitive ratio on accommodating sequences, which is bounded below by a constant. It is also shown that the worst order ratio for seat reservation algorithms is very closely related to the competitive ratio on accommodating sequences. © Springer-Verlag Berlin Heidelberg 2004.