A tight bound on the number of mobile servers to guarantee transferability among dominating configurations

In this paper, we propose a new framework to provide continuous services to users by a collection of mobile servers distributed over an interconnection network. We model those mobile servers as a subset of nodes, and assume that a user can receive the service if at least one adjacent node (including itself) plays the role of a server; i.e., we assume that the service could not be routed via the interconnection network. The main results obtained in this paper are summarized as follows: For the class of trees consisting of nn nodes, ⌊n/2⌋⌊n/2⌋ mobile servers are sometimes necessary and always sufficient to realize continuous services by the mobile servers, and for the class of Hamiltonian graphs with nn nodes, ⌈(n+1)/3⌉⌈(n+1)/3⌉ mobile servers are sometimes necessary and always sufficient.