- Tight Bounds on the Competitive Ratio on Accommodating Sequences
for the Seat Reservation Problem
- Eric Bach, Joan Boyar, Leah Epstein, Lene M. Favrholdt, Tao Jiang,
Kim S. Larsen, Guo-Hui Lin, Rob van Stee
Journal of Scheduling, 6(2): 131-147, 2003.
The unit price seat reservation problem is investigated.
The seat reservation problem is the problem of
assigning seat numbers on-line to requests for reservations
in a train traveling through k stations.
We are considering the version where all tickets have the
same price and where requests are treated fairly,
i.e., a request which can be fulfilled must be granted.
For fair deterministic algorithms,
we provide an asymptotically matching upper bound to the existing lower bound
which states that all fair algorithms for this problem
are 1/2-competitive on accommodating sequences, when
there are at least three seats.
Additionally, we give an asymptotic
upper bound of 7/9
for fair randomized algorithms against oblivious adversaries.
We also examine concrete on-line algorithms, First-Fit and Random,
for the special case of two seats.
Tight analyses of their performance are given.
The publication is available at www.springerlink.com (subscription may be required).