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

Authors:
Eric Bach;Joan Boyar;Leah Epstein;Lene M. Favrholdt;Tao Jiang;Kim S. Larsen;Guo-Hui Lin;Rob van Stee
Affiliations:
Computer Sciences Department, University of Wisconsin--Madison, 1210 West Dayton Street, Madison, WI;Department of Mathematics and Computer Science, University of Southern Denmark, Main Campus: Odense University, Campusvej 55, DK-5230 Odense M, Denmark;School of Computer and Media Sciences, The Interdisciplinary Center, P.O. Box 167, 46150 Herzliya, Israel;Department of Mathematics and Computer Science, University of Southern Denmark, Main Campus: Odense University, Campusvej 55, DK-5230 Odense M, Denmark;Department of Computer Science, University of California, Riverside;Department of Mathematics and Computer Science, University of Southern Denmark, Main Campus: Odense University, Campusvej 55, DK-5230 Odense M, Denmark;Department of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, and Department of Computing and Software, McMaster University, Canada;Centre for Mathematics and Computer Science (CWI), P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
Venue:
Journal of Scheduling - Special issue: On-line algorithm part I
Year:
2003

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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 ½-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.