Approximation Algorithms for Certain Network Improvement Problems

We study budget constrained network upgrading problems Such problems aim at nding optimal strategies for improving a network under some cost measure subject to certain budget constraints Given an edge weighted graph G V E in the edge based upgrading model it is assumed that each edge e of the given network also has an associated function ce t that speci es the cost of upgrading the edge by an amount t A reduction strategy speci es for each edge e the amount by which the length e is to be reduced In the node based upgrading model a node v can be upgraded at an expense of c v Such an upgrade reduces the delay of each edge incident on v For a given budget B the goal is to nd an improvement strategy such that the total cost of reduction is at most the given budget B and the cost of a subgraph e g minimum spanning tree under the modi ed edge lengths is the best over all possible strategies which obey the budget constraint After providing a brief overview of the models and de nitions of the various problems considered we present several new results on the complexity and approximability of network improvement problems