RANDOMIZED k-SERVER ALGORITHMS FOR GROWTH-RATE BOUNDED GRAPHS MANOR MENDEL Abstract. The paper referred to in the title is withdrawn.

The paper “Randomized k-server algorithms for growth-rate bounded graphs” by Y. Bartal and M. Mendel contains a serious error which the authors are unable to fix, and is therefore withdrawn. Versions of the paper appeared in (i) SODA ’04 (Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms), pp. 659–664; (ii) J. Algorithms 55 (2005) pp. 192–202; and (iii) arXiv:cs/0406033v1. All of them are flawed. Following is a technical description of the problem which refer to the arXiv version. Consider the description of the Demand-Marking Algorithm (DM) on Page 5 in the following setting: The phase begins and DM has no server in block B1 . Suppose the first request is for a point in B1 . According to the definition of DM, when δ > 1, dem1 = 0, since it finished only one 1-phase. Therefore, no server is brought to B1 , which is impossible. The analysis has related flaws. Consider the case when Dp (i) > 0, but at the end of period p there is only one Dp (i)-phase in block Bi . It may be the case that Cp−1 (i) = Dp (i), and the adversary did not have to move any of its servers in Bi during the p-th period. This is in contrast to the analysis in the proof of Lemma 10 which charge the adversary with a cost of δ on this period. Acknowledgments. The authors are grateful to Adam kalai and Duru Turkoglu for bringing those issues to their attention. The Open University of Israel E-mail address: [email protected]

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