Abstract
We show that the multi-criteria generalized Steiner network problem with ℓ≥2 cost functions has a polynomial-time ℓ-approximation algorithm. This generalizes the celebrated result of Jain for a single cost function. We also show that the approximation factor is tight for the natural LP relaxation. The problem is motivated by network design where multiple players have different or competing valuations and must agree on a common network (e.g., infrastructure design).
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