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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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This content will become publicly available on July 10, 2026
Polarization purity and cross-channel intensity correlations
We consider the question of monitoring polarization purity, that is, measuring deviations from orthogonalityδτandδϵof an ostensibly orthogonal polarization basis with a reference channel of ellipticityϵand tiltτ. A simple result was recently derived for a phase-sensitive receiver observing unpolarized radiation [IEEE Trans. Geosci. Remote Sens.62,2003610(2024)10.1109/TGRS.2024.3380531]: withρ(1)denoting the Pearson complex correlation coefficient between channelcomplex fields, it states that ∓cos(2ϵ)δτ±iδϵ≈ρ(1)whenδτ,ϵ≪1. However, phase-sensitive (in-phase and quadrature) data are seldom available at optical frequencies. To that end, here we generalize the result by deriving a new equation for the polarization “alignment” error:cos2(2ϵ)δτ2+δϵ2≈ρ(2), whereρ(2)is the intensity cross-correlation coefficient. Only the measurement of the(real) intensitycross-correlation coefficient is needed when observing unpolarized light. For the special case of a linearly polarized basis, the tilt error is simplyδτ≈ρ(2), and for the circular basis case, with ellipticity deviationδϵfrom circular helicityπ/4 (the reference channel of opposite helicity),δϵ≈ρ(2). These results provide simple means to gauge the quality of polarimeters and depolarizers.
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- Award ID(s):
- 2217182
- PAR ID:
- 10614632
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Journal of the Optical Society of America A
- Volume:
- 42
- Issue:
- 8
- ISSN:
- 1084-7529; JOAOD6
- Format(s):
- Medium: X Size: Article No. 1077
- Size(s):
- Article No. 1077
- Sponsoring Org:
- National Science Foundation
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