Minimizing pigeons for 2-hop and multihop demands is NP-hard, but a polynomial-time demand-aggregation algorithm achieves a 2-approximation.
1976.Queueing Systems, Volume II: Computer Applications
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The Carrier Pigeon Internet Protocol: An Algorithmic (and Lighthearted) Perspective
Minimizing pigeons for 2-hop and multihop demands is NP-hard, but a polynomial-time demand-aggregation algorithm achieves a 2-approximation.