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 Olkn. Examples are provided to illustrate the performance of the proposed algorithm.
Highlights
The classical location theory is concerned with the location of a service facility on a network
The location of special types of subgraphs such as paths, trees, or forests is considered as an extensive facility location problem
We considered the problem of optimally locating a service facility in a tree network with unreliable edges
Summary
The classical location theory is concerned with the location of a service facility on a network. The reliable (k, l)−tree core problem is stated as finding the optimal location of a tree-shaped facility (service provider) in an unreliable tree network with a diameter of at most l and having k leaves which maximizes the expected number of nodes that are reachable from it. This problem considers only edge failures while the nodes and the service provider facility are considered perfectly reliable.
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