## Non-Abusiveness Helps: An O(1)-Competitive Algorithm for Minimizing the Maximum Flow Time in the Online Traveling Salesman Problem

Please always quote using this URN: urn:nbn:de:0297-zib-7038

- 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 \emph{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 non-abusive adversary.

Author: | Sven O. Krumke, Luigi Laura, Maarten Lipmann, Alberto Marchetti-Spaccamela, Willem E. de Paepe, Diana Poensgen, Leen Stougie |
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Document Type: | ZIB-Report |

Tag: | Comparative Analysis; Competitive Analysis; Online Algorithms |

MSC-Classification: | 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C27 Combinatorial optimization |

90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C59 Approximation methods and heuristics | |

Date of first Publication: | 2002/10/18 |

Series (Serial Number): | ZIB-Report (02-36) |

Published in: | Appeared in: Proc. of the 5th Int. Workshop on Approximation Algorithms for Combinatorial Optimization. Springer 2002. LNCS, 2462, pp. 200-214 |