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

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish
Pages (from-to)131-147
Number of pages17
JournalJournal of Scheduling
Volume6
Issue number2
DOIs
StatePublished - Mar 2003
Externally publishedYes

Bibliographical note

Funding Information:
Eric Bach was supported in part by NSF Grant CCR-9510244. Joan Boyar would like to thank Faith Fich for interesting discussions regarding the seat reservation problem with n 2 seats. Joan Boyar and Kim S. Larsen carried out part of this work while visiting the Department of Computer Sciences, University of Wisconsin—Madison. They were supported in part by SNF (Denmark), in part by NSF (US) grant CCR-9510244, in part by the ESPRIT Long Term Research Programme of the EU under project number 20244 (ALCOM-IT). Joan Boyar, Lene M. Favrholdt, and Kim S. Larsen were supported in part by the IST Programme of the EU under contract number IST-1999-14186 (ALCOM-FT). Tao Jiang and Guo-Hui Lin were supported in part by NSERC Research Grant OGP0046613 and a CITO grant. Tao Jiang was supported in part by a UCR startup grant. Rob van Stee was supported by the Netherlands Organization for Scientific Research (NWO), project number SION 612-30-002.

Keywords

  • Accomodating sequences
  • Competitive ratio
  • On-line algorithms
  • Seat reservation problem

ASJC Scopus subject areas

  • Software
  • Engineering (all)
  • Management Science and Operations Research
  • Artificial Intelligence

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