Hofri, MichaShachnai, Hadas2017-08-022017-08-021998-02-02Hofri, Micha and Shachnai, Hadas. "The List Update ProblemImproved Bounds for the Counter Scheme." (1998) https://hdl.handle.net/1911/96483.https://hdl.handle.net/1911/96483We consider the problem of dynamic reorganization of a linear list, where requests for the elements are generated randomly with fixed, unknown probabilities. The objective is to obtain the smallest expected cost per access. It has been shown, that when no a-priori information is given on the reference probabilities, the Counter Scheme (CS) provides an optimal reorganization rule, which applies to {\em all} possible distributions. In this paper we show that for a list of n elements, arbitrary probabilities and any alpha in (0,1), the cost under CS approaches the minimal expected cost up to a ratio of 1 + alpha in O(n lg n alpha^2) reorganization steps.9 ppengYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, but this permission is only for a period of forty-five (45) days from the most recent time that you verified that this technical report is still available from the Computer Science Department of Rice University under terms that include this permission. All other rights are reserved by the author(s).Technical reportTR98-300