Work-Function Algorithm for k-Servers

Synonyms: none.

Years and Authors of Summarized Original Work

1994; Koutsoupias, Papadimitriou

Problem Definition

In the k-Server Problem, the task is to schedule the movement of k-servers in a metric space $\mathbb{M}$ in response to a sequence $\varrho = r_{1},r_{2},\ldots ,r_{n}$ of requests, where $r_{i} \in \mathbb{M}$ for all i. The servers initially occupy some configuration $X_{0} \subseteq \mathbb{M}$. After each request r _i is issued, one of the k-servers must move to r _i . A scheduleS specifies which server moves to each request. The task is to compute a schedule with minimum cost, where the cost of a schedule is defined as the total distance traveled by the servers. The example below shows a schedule for 2 servers on a sequence of requests (Fig. 1).

Fig. 1

A schedule for 2 servers on a request sequence $\varrho = r_{1},r_{2},\ldots ,r_{7}$. The initial configuration is $X_{0} = \left \{x_{1},x_{2}\right \}$. Server 1 serves r ₁, r ₂, r ₅, r ₆, while server 2...