## Probabilistic Competitive Analysis of a Dial-a-Ride Problem on Trees Under High Load

Please always quote using this URN: urn:nbn:de:0297-zib-8896

- In this paper we consider a simple variant of the Online Dial-a-Ride Problem from a probabilistic point of view. To this end, we look at a probabilistic version of this online Dial-a-Ride problem and introduce a probabilistic notion of the competitive ratio which states that an algorithm performs well on the vast majority of the instances. Our main result is that under the assumption of high load a certain online algorithm is probabilistically $(1+o(1))$-competitive if the underlying graph is a tree. This result can be extended to general graphs by using well-known approximation techniques at the expense of a distortion factor~$O(\log\|V\|)$.

Author: | Benjamin Hiller |
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Document Type: | ZIB-Report |

Tag: | Dial-a-Ride problem; IGNORE strategy; online algorithms; probabilistic competitive analysis |

MSC-Classification: | 68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68Qxx Theory of computing / 68Q25 Analysis of algorithms and problem complexity [See also 68W40] |

68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68Wxx Algorithms (For numerical algorithms, see 65-XX; for combinatorics and graph theory, see 05C85, 68Rxx) / 68W25 Approximation algorithms | |

CCS-Classification: | F. Theory of Computation / F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY (B.6-7, F.1.3) / F.2.2 Nonnumerical Algorithms and Problems (E.2-5, G.2, H.2-3) |

Date of first Publication: | 2005/12/09 |

Series (Serial Number): | ZIB-Report (05-56) |