Abstract
In the online traveling salesman problem OlTsp requests for visits to cities arrive online while the salesman is traveling. We study the F max-OlTsp where the objective is to minimize the maximum flow time. This objective is particularly interesting for applications. Unfortunately, there can be no competitive algorithm, neither deterministic nor randomized. Hence, competitive analysis fails to distinguish online algorithms. Not even resource augmentation which is helpful in scheduling works as a remedy. This unsatisfactory situation motivates the search for alternative analysis methods.
We introduce a natural restriction on the adversary for the F max-OlTsp on the real line. A non-abusive adversary may only move in a direction if there are yet unserved requests on this side. Our main result is an algorithm which achieves a constant competitive ratio against the nonabusive adversary.
Research supported by the German Science Foundation (DFG, grant GR 883/10)
Supported by the TMR Network DONET of the European Community ERB TMRXCT98- 0202
Partially supported by Algorithmic Methods for Optimizing the Railways in Europe (AMORE) grant HPRN-CT-1999-00104
Partially supported by Algorithmic Methods for Optimizing the Railways in Europe (AMORE) grant HPRN-CT-1999-00104
Supported by the TMR Network DONET of the European Community ERB TMRXCT98- 0202
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References
N. Ascheuer, S. O. Krumke, and J. Rambau. Online dial-a-ride problems: Minimizing the completion time. In Proceedings of the 17th International Symposium on Theoretical Aspects of Computer Science, volume 1770 of Lecture Notes in Computer Science, pages 639–650. Springer, 2000.
G. Ausiello, E. Feuerstein, S. Leonardi, L. Stougie, and M. Talamo. Algorithms for the on-line traveling salesman. Algorithmica, 29(4):560–581, 2001.
M. Blom, S. O. Krumke, W. E. de Paepe, and L. Stougie. The online-TSP against fair adversaries. Informs Journal on Computing, 13(2):138–148, 2001.
A. Borodin and R. El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, 1998.
E. Feuerstein and L. Stougie. On-line single server dial-a-ride problems. Theoretical Computer Science, 2001. To appear.
D. Hauptmeier, S. O. Krumke, and J. Rambau. The online dial-a-ride problem under reasonable load. Theoretical Computer Science, 2001. A preliminary version appeared in the Proceedings of the 4th Italian Conference on Algorithms and Complexity, 2000, vol. 1767 of Lecture Notes in Computer Science.
H. Kellerer, Th. Tautenhahn, and G. J. Woeginger. Approximability and nonapproximability results for minimizing total flow time on a single machine. In Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, pages 418–426, 1996.
E. Koutsoupias and C. Papadimitriou. Beyond competitive analysis. In Proceedings of the 35th Annual IEEE Symposium on the Foundations of Computer Science, pages 394–400, 1994.
S. O. Krumke, W. E. de Paepe, D. Poensgen, and L. Stougie. News from the online traveling repairman. In Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science, volume 2136 of Lecture Notes in Computer Science, pages 487–499, 2001.
R. Motwani and P. Raghavan. Randomized Algorithms. Cambridge University Press, 1995.
K. Pruhs and B. Kalyanasundaram. Speed is as powerful as clairvoyance. In Proceedings of the 36th Annual IEEE Symposium on the Foundations of Computer Science, pages 214–221, 1995.
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Krumke, S.O. et al. (2002). Non-abusiveness Helps: An % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbuLwBLnhiov2DGi1BTfMBaeHb % d9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe % pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaadeWaaq % aadaqbaaGcbaGaaGOmamaaCaaaleqabaGagiiBaWMaei4Ba8Maei4z % aCgaaOWaaWbaaSqabeaadaahaaadbeqaamaaBaaabaWaaWbaaeqaba % GaaGymaiabgkHiTiabgIGiodaaaeqaaaaaaaGcdaahaaWcbeqaaiab % d6gaUbaaaaa!4546! \[ 2^{\log } ^{^{_{^{1 - \in } } } } ^n \] (1)-Competitive Algorithm for Minimizing the Maximum Flow Time in the Online Traveling Salesman Problem. In: Jansen, K., Leonardi, S., Vazirani, V. (eds) Approximation Algorithms for Combinatorial Optimization. APPROX 2002. Lecture Notes in Computer Science, vol 2462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45753-4_18
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DOI: https://doi.org/10.1007/3-540-45753-4_18
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