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Better Bounds on the Accommodating Ratio for the Seat Reservation Problem

Extended Abstract
  • Eric Bach
  • Joan Boyar
  • Tao Jiang
  • Kim S. Larsen
  • Guo-Hui Lin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1858)

Abstract

In a recent paper [J. Boyar and K.S. Larsen, The seat reservation problem, Algorithmica, 25(1999), 403–417], the seat reservation problem was investigated. It was shown that for the unit price problem, where all tickets have the same price, all “fair” algorithms are at least 1/2-accommodating, while no fair algorithm is more than (4/5+O(1/k))-accommodating, where k is the number of stations the train travels. In this paper, we design a more dextrous adversary argument, such that we improve the upper bound on the accommodating ratio to (7/9+O(1/k)), even for fair randomized algorithms against oblivious adversaries. For deterministic algorithms, the upper bound is lowered to approximately .7699. It is shown that better upper bounds exist for the special cases with n = 2, 3, and 4 seats. A concrete on-line deterministic algorithm First-Fit and an on-line randomized algorithm Random are also examined for the special case n = 2, where they are shown to be asymptotically optimal.

Keywords

The seat reservation problem on-line algorithms accommodating ratio adversary argument 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Eric Bach
    • 1
  • Joan Boyar
    • 2
  • Tao Jiang
    • 3
    • 4
  • Kim S. Larsen
    • 2
  • Guo-Hui Lin
    • 3
    • 5
  1. 1.Computer Sciences DepartmentUniversity of Wisconsin - MadisonMadison
  2. 2.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdenseDenmark
  3. 3.Department of Computer ScienceUniversity of CaliforniaRiverside
  4. 4.Department of Computing and SoftwareMcMaster UniversityHamiltonCanada
  5. 5.Department of Computer ScienceUniversity of WaterlooWaterlooCanada

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