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The use of Lagrange multiplier offsets improves the iterative water-filling algorithm for digital subscriber line systems. We present a technique for generating constant offsets using a virtual network of reference lines. We provide simulation results that show that the achievable performance is very close to that of existing state-of-the-art algorithms, while requiring significantly fewer time-consuming interference measurements and reducing the amount of message passing required.Index Terms-Digital subscriber line, dynamic spectrum management, power allocation, resource allocation.