Elsevier

Journal of Algorithms

Volume 52, Issue 2, August 2004, Pages 169-192
Journal of Algorithms

Seat reservation allowing seat changes

https://doi.org/10.1016/j.jalgor.2004.02.002Get rights and content

Abstract

We consider a variant of the Seat Reservation Problem [J. Boyar, K.S. Larsen, Algorithmica 25 (1999) 403–417] in which seat changes are allowed. We analyze the model using the competitive ratio, the competitive ratio on accommodating sequences [J. Boyar, K.S. Larsen, Algorithmica 25 (1999) 403–417], and the accommodating function [J. Boyar et al., Acta Informatica 40 (2003) 3–35; J. Boyar et al., SIAM J. Comput. 31 (1) (2001) 233–258]. A very promising family of algorithms considered in this paper is Min-Change, which will ask passengers to change seats, only if they would otherwise have been rejected. Min-Change belongs to a large class of conservative algorithms, which all have very high performance guarantees. For instance, if the optimal off-line algorithm can seat all of the passengers, 2/3 of the passengers can be seated on-line using any conservative algorithm allowing only one seat change and 3/4 will be seated if two seat changes are allowed. This should be compared to the asymptotic hardness result of 1/2 for the best algorithm when no seat changes are allowed [E. Bach et al., J. Sched. 6 (2003) 131–147]. Another interesting algorithm, Modified-Kierstead–Trotter, is proposed and shown to seat all passengers if the optimal off-line algorithm could have accommodated them with only half as many seats. On this type of sequence, Modified-Kierstead–Trotter is strictly better than Min-Change-First-Fit which is strictly better than the Checkerboard algorithm.

References (13)

  • E Bach et al.

    Tight bounds on the competitive ratio on accommodating sequences for the seat reservation problem

    J. Sched.

    (2003)
  • J Boyar et al.

    Fair versus unrestricted bin packing

    Nordic J. Comput.

    (2001)
  • J Boyar et al.

    Extending the accommodating function

    Acta Informatica

    (2003)
  • J. Boyar, S. Krarup, M.N. Nielsen, Seat reservation allowing seat changes, Preprint PP–2002–06, Department of Computer...
  • J Boyar et al.

    The seat reservation problem

    Algorithmica

    (1999)
  • J Boyar et al.

    The accommodating function: a generalization of the competitive ratio

    SIAM J. Comput.

    (2001)
There are more references available in the full text version of this article.

Cited by (0)

A preliminary version of some of these results was presented at Workshop on Algorithmic Methods and Models for Optimization of Railways, ATMOS 2001, and appeared in: Proceedings of the Satellite Workshops of the 28th International Colloquium on Automata, Languages, and Programming, in: Electronic Notes in Theoretical Computer Science, vol. 50, Elsevier, 2001, pp. 26–40.

1

Supported in part by the Danish Natural Science Research Council (SNF) and in part by the Future and Emerging Technologies program of the EU under contract number IST-1999-14186 (alcom-ft).

View full text