On the Location of a Constrained k - Tree Facility in a Tree Network with Unreliable Edges

Abstract

Given a tree network $T$ with $n$ vertices where each edge has an independent operational probability, we are interested in finding the optimal location of a reliable service provider facility in a shape of subtree with exactly $k$ leaves and with a diameter of at most $l$ which maximizes the expected number of nodes that are reachable from the selected subtree by operational paths. Demand requests for service originate at perfectly reliable nodes. So, the major concern of this paper is to find a location of a reliable tree-shaped facility on the network in order to provide a maximum access to network services by ensuring the highest level of network connectivity between the demand nodes and the facility. An efficient algorithm for finding a reliable $(k,l)$ – tree core of $T$ is developed. The time complexity of the proposed algorithm is $O\left(lkn\right).$ Examples are provided to illustrate the performance of the proposed algorithm.