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Our symmetry-free model for spectrum allocation (SA) in networks of general topology leverages two properties: (1) SA is equivalent to a connection permutation problem, and (2) in assigning spectrum, it is sufficient to consider the allocation made by the first-fit (FF) algorithm. This model opens up algorithmic approaches that altogether sidestep spectrum symmetry, i.e., eliminate from consideration the exponential number of equivalent solutions resulting from spectrum slot permutations. Recursive FF (RFF) is such an algorithm; it applies FF recursively to search the connection permutation space and solve the SA problem optimally. Moreover, parallelism is inherent in the spectrum symmetry-free model, as the connection permutation space may be naturally decomposed into non-overlapping subsets that can be searched independently. Accordingly, RFF admits multi-threaded implementations that may be tailored to the computing environment at hand. In this work, we present two strategies for parallelizing the execution of RFF, and we evaluate them experimentally using a comprehensive set of metrics. Our experiments indicate that RFF explores a vast number of symmetry-free solutions, and for moderate-sized networks, it takes mere seconds to yield solutions that are either optimal or very close to the lower bound.
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Recursive first fit: a highly parallel optimal solution to spectrum allocation
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.
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- Award ID(s):
- 1907142
- PAR ID:
- 10369463
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Journal of Optical Communications and Networking
- Volume:
- 14
- Issue:
- 4
- ISSN:
- 1943-0620; JOCNBB
- Format(s):
- Medium: X Size: Article No. 165
- Size(s):
- Article No. 165
- Sponsoring Org:
- National Science Foundation
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