Building Edge-Failure Resilient Networks
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
An improved approximation algorithm for virtual private network design
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Maximizing restorable throughput in MPLS networks
IEEE/ACM Transactions on Networking (TON)
Robust network codes for unicast connections: a case study
IEEE/ACM Transactions on Networking (TON)
New approaches for virtual private network design
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Structure-Based resilience metrics for service-oriented networks
EDCC'05 Proceedings of the 5th European conference on Dependable Computing
Stable routing under the Spanning Tree Protocol
Operations Research Letters
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We examine various problems concerning the reservation of capacity in a given network, where each arc has a per-unit cost, so as to be "resilient" against one or more arc failures. For a given pair (s,t) of nodes and demand T, we require that, on the failure of any k arcs of the network, there is sufficient reserved capacity in the remainder of the network to support an (s,t) flow of value T. This problem can be solved in polynomial time for any fixed k, but we show that it is NP-hard if we are required to reserve an integer capacity on each arc. We concentrate on the case where the reservation has to consist of a collection of arc-disjoint paths: here we give a very simple algorithm to find a minimum cost fractional solution, based on finding successive shortest paths in the network. Unlike traditional network flow problems, the integral version is NP-hard: we do, however, give a polynomial time $\frac{15}{14}$-approximation algorithm in the case k=1 and show that this bound is best possible unless P = NP.