Online Scheduling for Sorting Buffers

Abstract

We introduce the online scheduling problem for sorting buffer. A service station and a sorting buffer are given. An input sequence of item which are only characterized by a specific attribute has to be processed by the service station which benefits from consecutive item with the same attribute value. The sorting buffer which is a random access buffer with storage capacity for k items can be used to rearrange the input sequence. The goal is to minimize the cost of the service station, i.e.,the number of maximal subsequence in it sequence of items containing only item with the same attribute value. This problem is motivated by many applications in computer science and economic .

The strategies are evaluated in a competitive analysis in which the cost of the online strategy is compared with the cost of an optimal online strategy. Our main result is a deterministic strategy that achieve a competitive ratio of O(log² k). In addition, we how that several standard strategie are unsuitable for this problem, i.e.,we prove a lower bound of Ω(√k )on the competitive ratio of the First In First Out (FIFO)and Least Recently Used (LRU)strategy and of Ω(k )on the competitive ratio of the Largest Color First (LCF)strategy.

The first two author are partially supported by the DFG-Sonderforschungsbereich 376,DFG grant 872/8-1,and the Future and Emerging Technologies program of the EU under contract number IST-1999-14186 (ALCOM-FT).The third author is supported by a fellowship within the ICSI-Postdoc-Program of the German Academic Exchange Service (DAAD).