Approximation Algorithms and Relaxations for a Service Provision Problem on a Telecommunication Network

Modern distributed telecommunication networks have widely extended the possibilities of the telecommunication industry for ooering a wide variety of services, directly or indirectly by facilitating them for other service providers. As new services are often processing based there is a need for a shift of focus in research from traditional transportation of information to processing of information. This paper considers the problem of installing software applications for services at the computing nodes of the distributed network, in order to maximize the service provider's proot when meeting demand. The service provision problem is formulated as an integer linear programming model and is shown to be NP-hard. We exploit similarities to the well-known (multiple) knapsack problem in devising approximation algorithms and analysing their performance from a worst case point of view. Among others a fully polynomial time approximation scheme is presented for the case with one computing node. The other main results of the paper concern the derivation of upper bounds on the optimal solution via LP and Lagrangian relaxations.