Reordering Buffer Management with Advice

In the reordering buffer management problem, a sequence of colored items arrives at a service station to be processed. Each color change between two consecutively processed items generates some cost. A reordering buffer of capacity k items can be used to preprocess the input sequence in order to decrease the number of color changes. The goal is to find a scheduling strategy that, using the reordering buffer, minimizes the number of color changes in the given sequence of items. We consider the problem in the setting of online computation with advice. In this model, the color of an item becomes known only at the time when the item enters the reordering buffer. Additionally, together A preliminary version of this paper appeared in the Proc. of the 11th Workshop on Approximation and Online Algorithms (WAOA 2013); LNCS, 2013, pp.132-143. The work performed while the first and the fourth author were at the Max-Planck-Institut für Informatik, Saarbrücken, Germany. The first author is supported by the DFF-MOBILEX mobility grant from the Danish Council for Independent Research. The second and third authors partially supported by ANR project NeTOC. Anna Adamaszek University of Copenhagen, Denmark E-mail: [email protected] Marc P. Renault CNRS, LIAFA, Université Paris Diderot – Paris 7, Sorbonne Paris-Cité, France E-mail: [email protected] Adi Rosén CNRS, LIAFA, Université Paris Diderot – Paris 7, Sorbonne Paris-Cité, France E-mail: [email protected] Rob van Stee University of Leicester, Leicester, United Kingdom E-mail: [email protected] with each item entering the buffer, we get a fixed number of advice bits, which can be seen as information about the future or as information about an optimal solution (or an approximation thereof) for the whole input sequence. We show that for any ε > 0 there is a (1 + ε)-competitive algorithm for the problem which uses only a constant (depending on ε) number of advice bits per input item. This immediately implies a (1 + ε)-approximation algorithm which has 2 log 1/ε) running time (this should be compared to the trivial optimal algorithm which has a running time of k). We complement the above result by presenting a lower bound of Ω(log k) bits of advice per request for any 1-competitive algorithm.