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

doi:10.1023/A:1022985808959

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 journal › Article › peer-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 language	English
Pages (from-to)	131-147
Number of pages	17
Journal	Journal of Scheduling
Volume	6
Issue number	2
DOIs	https://doi.org/10.1023/A:1022985808959
State	Published - Mar 2003
Externally published	Yes

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
General Engineering
Management Science and Operations Research
Artificial Intelligence

Access to Document

10.1023/A:1022985808959

Cite this

@article{797c928519a94fc9ae9e53b82ee2ab5e,

title = "Tight bounds on the competitive ratio on accommodating sequences for the seat reservation problem",

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.",

keywords = "Accomodating sequences, Competitive ratio, On-line algorithms, Seat reservation problem",

author = "Eric Bach and Joan Boyar and Leah Epstein and Favrholdt, {Lene M.} and Tao Jiang and Larsen, {Kim S.} and Lin, {Guo Hui} and {Van Stee}, Rob",

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.",

year = "2003",

month = mar,

doi = "10.1023/A:1022985808959",

language = "English",

volume = "6",

pages = "131--147",

journal = "Journal of Scheduling",

issn = "1094-6136",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Tight bounds on the competitive ratio on accommodating sequences for the seat reservation problem

AU - Bach, Eric

AU - Boyar, Joan

AU - Epstein, Leah

AU - Favrholdt, Lene M.

AU - Jiang, Tao

AU - Larsen, Kim S.

AU - Lin, Guo Hui

AU - Van Stee, Rob

N1 - 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.

PY - 2003/3

Y1 - 2003/3

N2 - 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.

AB - 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.

KW - Accomodating sequences

KW - Competitive ratio

KW - On-line algorithms

KW - Seat reservation problem

UR - http://www.scopus.com/inward/record.url?scp=3042729845&partnerID=8YFLogxK

U2 - 10.1023/A:1022985808959

DO - 10.1023/A:1022985808959

M3 - Article

AN - SCOPUS:3042729845

SN - 1094-6136

VL - 6

SP - 131

EP - 147

JO - Journal of Scheduling

JF - Journal of Scheduling

IS - 2

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this