# Network Resilience Assessment via QoS Degradation Metrics: An Algorithmic Approach

This paper focuses on network resilience to perturbation of edge weight. Other than connectivity, many network applications nowadays rely upon some measure of network distance between a pair of connected nodes. In these systems, a metric related to network functionality is associated to each edge. A pair of nodes only being functional if the weighted, shortest-path distance between the pair is below a given threshold T. Consequently, a natural question is on which degree the change of edge weights can damage the network functionality? With this motivation, we study a new problem, Quality of Service Degradation: given a set of pairs, find a minimum budget to increase the edge weights which ensures the distance between each pair exceeds T. We introduce four algorithms with theoretical performance guarantees for this problem. Each of them has its own strength in trade-off between effectiveness and running time, which are illustrated both in theory and comprehensive experimental evaluation.

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