Generalized Two-Server Problem

Years and Authors of Summarized Original Work

• 2006; Sitters, Stougie

Problem Definition

In the generalized two-server problem, we are given two servers: one moving in a metric space $\mathbb{X}$ and one moving in a metric space $\mathbb{Y}$. They are to serve requests $r \in \mathbb{X} \times \mathbb{Y}$ which arrive one by one. A request r = (x, y) is served by moving either the $\mathbb{X}$-server to point x or the $\mathbb{Y}$-server to point y. The decision as to which server to move to the next request is irrevocable and has to be taken without any knowledge about future requests. The objective is to minimize the total distance traveled by the two servers (Fig. 1).

Generalized Two-Server Problem, Fig. 1

In this example, both servers move in the plane and start from the configuration (x₀, y₀). The $\mathbb{X}$-server moves through requests 1 and 3, and the $\mathbb{Y}$-server takes care of requests 2 and 4. The cost of this solution is the sum of the path-lengths