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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). 

With the ever-increasing size of training models and datasets, network communication has emerged as a major bottleneck in distributed deep learning training. To address this challenge, we propose an optical distributed deep learning (ODDL) architecture. ODDL utilizes a fast yet scalable all-optical network architecture to accelerate distributed training. One of the key features of the architecture is its flow-based transmit scheduling with fast reconfiguration. This allows ODDL to allocate dedicated optical paths for each traffic stream dynamically, resulting in low network latency and high network utilization. Additionally, ODDL provides physically isolated and tailored network resources for training tasks by reconfiguring the optical switch using LCoS-WSS technology. The ODDL topology also uses tunable transceivers to adapt to time-varying traffic patterns. To achieve accurate and fine-grained scheduling of optical circuits, we propose an efficient distributed control scheme that incurs minimal delay overhead. Our evaluation on real-world traces showcases ODDL’s remarkable performance. When implemented with 1024 nodes and 100 Gbps bandwidth, ODDL accelerates VGG19 training by 1.6× and 1.7× compared to conventional fat-tree electrical networks and photonic SiP-Ring architectures, respectively. We further build a four-node testbed, and our experiments show that ODDL can achieve comparable training time compared to that of anidealelectrical switching network. 

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. 

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.