Network Resilience and the Length-Bounded Multicut Problem

Motivated by networked systems in which the functionality of the network depends on vertices in the network being within a bounded distance T of each other, we study the length-bounded multicut problem: given a set of pairs, find a minimum-size set of edges whose removal ensures the distance between each pair exceeds T. We introduce the first algorithms for this problem capable of scaling to massive networks with billions of edges and nodes: three highly scalable algorithms with worst-case performance ratios. Furthermore, one of our algorithms is fully dynamic, capable of updating its solution upon incremental vertex / edge additions or removals from the network while maintaining its performance ratio. Finally, we show that unless NP ⊆ BPP, there is no polynomial-time, approximation algorithm with performance ratio better than $Ømega (T)$, which matches the ratio of our dynamic algorithm up to a constant factor.

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