An Efficient Algorithm for Computing Network Reliability in Small Treewidth

We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge appears in the network with its associated probability and the problem is to determine the probability of having at least one source-to-target path. This problem is known to be NP-hard. We present a linear-time fixed-parameter algorithm based on a parameter called treewidth, which is a measure of tree-likeness of graphs. Network Reliability was already known to be solvable in polynomial time for bounded treewidth, but there were no concrete algorithms and the known methods used complicated structures and were not easy to implement. We provide a significantly simpler and more intuitive algorithm that is much easier to implement. We also report on an implementation of our algorithm and establish the applicability of our approach by providing experimental results on the graphs of subway and transit systems of several major cities, such as London and Tokyo. To the best of our knowledge, this is the first exact algorithm for Network Reliability that can scale to handle real-world instances of the problem.Comment: 14 page

A framework for the joint placement of edge service infrastructure and User Plane Functions for 5G

Achieving less than 1 ms end-to-end communication latency, required for certain 5G services and use cases, is imposing severe technical challenges for the deployment of next-generation networks. To achieve such an ambitious goal, the service infrastructure and User Plane Function (UPF) placement at the network edge, is mandatory. However, this solution implies a substantial increase in deployment and operational costs. To cost-effectively solve this joint placement problem, this paper introduces a framework to jointly address the placement of edge nodes (ENs) and UPFs. Our framework proposal relies on Integer Linear Programming (ILP) and heuristic solutions. The main objective is to determine the ENs and UPFs’ optimal number and locations to minimize overall costs while satisfying the service requirements. To this aim, several parameters and factors are considered, such as capacity, latency, costs and site restrictions. The proposed solutions are evaluated based on different metrics and the obtained results showcase over 20% cost savings for the service infrastructure deployment. Moreover, the gap between the UPF placement heuristic and the optimal solution is equal to only one UPF in the worst cases, and a computation time reduction of over 35% is achieved in all the use cases studied.Postprint (author's final draft

Exact two-terminal reliability of some directed networks

The calculation of network reliability in a probabilistic context has long been an issue of practical and academic importance. Conventional approaches (determination of bounds, sums of disjoint products algorithms, Monte Carlo evaluations, studies of the reliability polynomials, etc.) only provide approximations when the network's size increases, even when nodes do not fail and all edges have the same reliability p. We consider here a directed, generic graph of arbitrary size mimicking real-life long-haul communication networks, and give the exact, analytical solution for the two-terminal reliability. This solution involves a product of transfer matrices, in which individual reliabilities of edges and nodes are taken into account. The special case of identical edge and node reliabilities (p and rho, respectively) is addressed. We consider a case study based on a commonly-used configuration, and assess the influence of the edges being directed (or not) on various measures of network performance. While the two-terminal reliability, the failure frequency and the failure rate of the connection are quite similar, the locations of complex zeros of the two-terminal reliability polynomials exhibit strong differences, and various structure transitions at specific values of rho. The present work could be extended to provide a catalog of exactly solvable networks in terms of reliability, which could be useful as building blocks for new and improved bounds, as well as benchmarks, in the general case