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Journal of Scheduling

, Volume 6, Issue 2, pp 131–147 | Cite as

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
Article

Abstract

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, that is, 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 \(\tfrac{1}{2}\)-competitive on accommodating sequences, when there are at least three seats.

Additionally, we give an asymptotic upper bound of \(\tfrac{7}{9}\) 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.

competitive ratio accomodating sequences on-line algorithms seat reservation problem 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Eric Bach
    • 1
  • Joan Boyar
    • 2
  • Leah Epstein
    • 3
  • Lene M. Favrholdt
    • 1
  • Tao Jiang
    • 3
  • Kim S. Larsen
    • 1
  • Guo-Hui Lin
    • 3
  • Rob van Stee
    • 4
  1. 1.Computer Sciences DepartmentUniversity of Wisconsin – MadisonMadisonUSA
  2. 2.Department of Mathematics and Computer ScienceUniversity of Southern Denmark, Main Campus: Odense University, Campusvej 55Odense MDenmark
  3. 3.School of Computer and Media SciencesThe Interdisciplinary CenterHerzliyaIsrael
  4. 4.Centre for Mathematics and Computer Science (CWI)AmsterdamThe Netherlands

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