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Scalable Recursive First Fit: An Optimal Solution to the Spectrum Allocation Problem

We revisit the classical spectrum allocation (SA) problem, a fundamental subproblem in optical network design, and make three contributions. First, we show how some SA problem instances may be decomposed into smaller instances that may be solved independently without loss of optimality. Second, we prove an optimality property of the well-known first-fit (FF) heuristic. Finally, we leverage this property to develop a recursive algorithm that applies the FF heuristic to find an optimal solution efficiently. This recursive first-fit (Rec-FF) algorithm complements our recent algorithm that recursively searches the routing space, and may be combined with it to solve large routing and spectrum allocation (RSA) problem instances to optimality.