Generalized reordering buffer management

An instance of the generalized reordering buffer management problem consists of a service station that has κ 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 κ = 1. In this paper, we develop a randomized online algorithm that obtains a competitive ratio of O(√ b ln κ). Note that this result beats the easy deterministic lower bound of κ whenever b < κ^2-ε. We complement our randomized approach by presenting a deterministic algorithm that attains a competitive ratio of O(min{κ²ln b, κb}). We further demonstrate that if our deterministic algorithm can employ κ/(1 - δ) servers where δ ∈ (0, 1), then it achieves a competitive ratio of O(min{ln b/δ², b/δ}) against an optimal offline adversary that employs κ servers.