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Providing approximate max-min fair bandwidth allocation among flows within a network or at a single router has been an important research problem. In this paper, we study the space complexity of fairness algorithms, and the communication complexity of distributed global fairness algorithms. We show that in order to enforce max-min fairness with bounded errors, a router must maintain per-flow state. Then we present a practical edge-marking based architecture to demonstrate the enforcement of approximate global max-min fairness for representative scenarios with multiple bottlenecks and non-responsive traffic. We validate our architecture using packet level simulations.