Algorithm DC-Tree for $\boldsymbol{k}$-Servers on Trees

Years and Authors of Summarized Original Work

• 1991; Chrobak, Larmore

Problem Definition

In the k-Server Problem, one wishes to schedule the movement of k-servers in a metric space $\mathbb{M}$, in response to a sequence ϱ = r₁, r₂, …, r _n of requests, where $r_{i} \in \mathbb{M}$ for each i. Initially, all the servers are located at some initial configuration $X_{0} \subseteq \mathbb{M}$ of k points. After each request r _i is issued, one of the k-servers must move to r _i . A schedule specifies which server moves to each request. The cost of a schedule is the total distance traveled by the servers, and our objective is to find a schedule with minimum cost.

Algorithm DC-Tree for -Servers on Trees, Fig. 1

Algorithm DC-Tree serving a request on r. The configuration before r is issued is on the left; the configuration after the service is completed is on the right. At first, all servers are active. When server 3 reaches point x, server 1 becomes inactive. When server 3 reaches point y...