Recursive first fit: a highly parallel optimal solution to spectrum allocation

Abstract

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 and parallel algorithm that applies the FF heuristic to find an optimal solution efficiently. This recursive FF algorithm is highly scalable because of two unique properties: (1) it completely sidesteps the symmetry inherent in SA and hence drastically reduces the solution space compared to typical integer linear programming formulations, and (2) the solution space can be naturally decomposed in non-overlapping subtrees that may be explored in parallel almost independently of each other, resulting in faster than linear speedup.