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First-fit (FF) is a well-known and widely deployed algorithm for spectrum assignment (SA), but until our recent study [J. Opt. Commun. Netw.14,165(2022)JOCNBB1943-062010.1364/JOCN.445492], investigations of the algorithm had been experimental in nature and no formal properties of the algorithm with respect to SA were known. In this work, we make two contributions. First, we show that FF is auniversalalgorithm for the SA problem in the sense that, for any variant, 1) it can be used to construct solutions equivalent to, or better than, any solution obtained by any other algorithm, and 2) it can construct an optimal solution. This universality property applies to both the min-max and min-frag objectives and to variants of the SA problem with or without guard band constraints. Consequently, the spectrum symmetry-free model of our recent study [J. Opt. Commun. Netw.14,165(2022)JOCNBB1943-062010.1364/JOCN.445492] extends to all known SA variants, which therefore reduce to permutation problems. Second, we extend the spectrum symmetry-free model to the routing and spectrum assignment (RSA) problem in general topologies. This model allows for the design of more efficient algorithms as it eliminates from consideration an exponential number of equivalent symmetric solutions. By sidestepping symmetry, the RSA solution space is naturally and optimally decomposed into a routing space and a connection permutation space. Building upon this property, we introduce a two-parameter, symmetry-freeuniversalalgorithm that can be used to tackle any RSA variant in a uniform manner. The algorithm is amenable to multi-threaded execution to speed up the search process, and the value of the parameters can be adjusted to strike a balance between running time and solution quality. Our evaluation provides insight into the relative benefits of path diversity (which determines the size of the routing space) and connection diversity (which determines the size of the permutation space).
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Symmetry-free algorithm for spectrum allocation: parallel implementations and evaluation
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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- Award ID(s):
- 1907142
- PAR ID:
- 10461996
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Journal of Optical Communications and Networking
- Volume:
- 15
- Issue:
- 10
- ISSN:
- 1943-0620; JOCNBB
- Format(s):
- Medium: X Size: Article No. E40
- Size(s):
- Article No. E40
- Sponsoring Org:
- National Science Foundation
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