Generalized Reordering Buffer Management

An instance of the generalized reordering buffer management problem consists of a service station that has k servers, each configured with a color, and a buffer of size b. The station needs to serve an online stream of colored items. Whenever an item arrives, it is stored in the buffer. At any point in time, a currently pending item can be served by switching a server to its color. The objective is to serve all items in a way that minimizes the number of servers color switches. This problem generalizes two well-studied online problems: the paging problem, which is the special case when b = 1, and the reordering buffer problem, which is the special case when k = 1. In this paper, we develop a randomized online algorithm that obtains a competitive ratio ofO( √ b ln k). Note that this result beats the easy deterministic lower bound of k whenever b < k2−ε. We complement our randomized approach by presenting a deterministic algorithm that attains a competitive ratio of O(min{k ln b, kb}). We further demonstrate that if our deterministic algorithm can employ k/(1 − δ) servers where δ ∈ (0, 1), then it achieves a competitive ratio of O(min{ln b/δ, b/δ}) against an optimal offline adversary that employs k servers. ∗Blavatnik School of Computer Science, Tel-Aviv University, Israel. Email: [email protected]. Supported in part by the Israel Science Foundation (grant No. 1404/10) and by the Israeli Centers of Research Excellence (I-CORE) program (Center No. 4/11). †Department of Computer Science and DIMAP, University of Warwick, UK. Email: [email protected]. Supported in part by EPSRC award EP/D063191/1 and EPSRC grant EP/F043333/1. ‡Yahoo! Research. Email: [email protected]. §Blavatnik School of Computer Science, Tel-Aviv University, Israel. Email: [email protected].