Multifiber Networks Research Articles

Zero-cost upgrade to a multi-fiber network with partial lane-change capabilities

Growing capacity requirements are leading to the deployment of multiple fibers in each optical network link. Even though deploying state-of-the-art multi-fiber network architectures with stacked and independent fiber layers simplifies network design and control, spectrum can be used more efficiently if the optical-network nodes allow fiber layers to be interconnected, i.e., if the so-called lane change is enabled. Unfortunately, lane change in high-degree optical nodes requires wavelength selective switches (WSSs) with a high number of ports, which is prohibitively costly or even unfeasible with current WSS technology. Instead, lane change in low-degree optical nodes can be enabled at no extra cost, using WSS ports that are otherwise left empty. In this study, we describe our proposal for a multi-fiber network with partial lane-change capabilities and perform a simulative study to identify the advantages of this architecture, as well as discuss the emerging resource allocation challenges associated with it. We demonstrate that, by enabling lane change in degree-2 nodes, we can increase network throughput by 3% and restore 5%–8% more traffic in the case of single- and double-link failures at no additional equipment cost.

Simulation of Coherent Electromagnetic Waves in Wavelength Division Multiplexing (WDM) Transmission

This study analyzes the application of Wavelength Division Multiplexing (WDM) in fiber optic networks which aims to find the wavelength, WDM optical spectrum and modes, as well as the CPR estimated phase and modes. In this study WDM allows the simultaneous transmission of different data streams through a single optical fiber, using different wavelengths. This research was conducted using the python OptiCommPy module. This module is used to perform modeling of complex optical fiber transmission systems by considering the various parameters and disturbances involved in optical transmission. The results obtained from this study are that WDM networks can use full or limited wavelength conversion, depending on the wavelength conversion capability of each network node. Whereas multifiber networks use fiber pools between network nodes, and multifiber WDM networks can be implemented without or with full wavelength conversion. This research can be a guide for designing coherent electromagnetic waves in WDM transmissions using the OptiCommPy python module.

Deep Machine Learning Algorithms in Glioblastoma (GBM) MRI evaluation (PL4.005)

<h3>Objective:</h3> To test the reliability of automatic segmentation models on post-operative MRIs in glioblastoma evaluation. <h3>Background:</h3> The extent of tumor resection in glioblastoma is an independent prognostic factor associated with clinical outcomes. Because radiological assessment to identify residual tumoral components can be time-consuming and subject to inter-rater variability, the implementation of artificial intelligence (AI) may improve radiological assessment. Hereby, we evaluate performance of different automatic brain tumor segmentation algorithms trained on pre-operative MRI datasets, on post-operative MRI scans of patients with glioblastoma. <h3>Design/Methods:</h3> We evaluated the performance of ten different deep-learning models designed for automated brain tumor segmentation. Models were trained using a publicly available dataset from the Brain Tumor Segmentation (BRaTS) Challenge 2020 and was tested in our institutional MRI scans including pre-operative and post-operative MRI examinations. Semiautomatic segmentation was performed in the institutional scans and was used as the ground truth. Dice Similarity Coefficient (DSC) was used to compare each model’s performance against the ground truth. <h3>Results:</h3> A total of 329 MR examinations were used for training purposes and a separate 100 scans were used to test the deep-learning algorithms. Overall, models demonstrated better performance on pre-operative scans. Among post-operative MRI studies, Knowledge Distillation algorithm exhibited the best performance with a DSC score of 0.836 for whole tumor segmentation. When evaluating specific regions within the tumor, Knowledge Distillation demonstrated a DSC of 0.82 for the FLAIR hyperintense region, 3D Dilated Multi-Fiber Network achieved a DSC of 0.88 in the contrast-enhancing tumoral region, and 3D U-Net exhibited the highest DCS for the non-enhancing core (0.84). <h3>Conclusions:</h3> Deep machine learning has the potential to quantify enhancing and FLAIR volumes in brain MRI from glioblastoma patients with high accuracy. Current automatic segmentation models can perform automatic segmentation on post-operative MRI scans with an 88% accuracy. Further investigations are needed to improve this promising AI technology. <b>Disclosure:</b> An immediate family member of Dr. Zhu has stock in Abbott lab. The institution of Dr. Zhu has received research support from NRG NIH. The institution of Dr. Zhu has received research support from Novocure, Inc. The institution of Dr. Zhu has received research support from Five Prime pharmaceutical. The institution of Dr. Zhu has received research support from Denovo, inc. The institution of Dr. Zhu has received research support from Boston Biomedical Sumitomo Dainippon Pharma Global Oncology. The institution of Dr. Zhu has received research support from CNS pharmaceutical. Mr. HSIEH has nothing to disclose. Ms. Kabir has nothing to disclose. Dr. Nunez has nothing to disclose. Carlos Rodriguez Quintero has nothing to disclose. Dr. Cai has nothing to disclose. Dr. Hsu has nothing to disclose. Dr. Arevalo has nothing to disclose. Kangyi Zhao has nothing to disclose. Jackie Jiaqi Zhang has nothing to disclose. Roy Riascos-Castaneda has nothing to disclose. The institution of Dr. Jiang has received research support from NIH. The institution of Dr. Jiang has received research support from CPRIT. The institution of Dr. Jiang has received research support from NSF. shayan shams has nothing to disclose.

An Adaptive Multiobjective Genetic Algorithm with Multi-Strategy Fusion for Resource Allocation in Elastic Multi-Core Fiber Networks

Core switching on different links in optical networks enables network operators to allocate network resources more flexibly, so as to reduce the network request blocking ratio under limited resources. Facing a differentiated network environment and diversified user demands, network operators need to optimize multiple objectives that are independent and diversionary of each other, and to provide multiple resource allocation schemes whose objective values do not dominate each other. For the static routing, spectrum, and core assignment (RSCA) problem in elastic optical networks with multi-core fiber (MCF-EONs), there is no literature that simultaneously considers core switching and multiobjective optimization algorithms. This paper improves the existing models and algorithms to adapt to the RSCA problem. In this paper, the RSCA problem is formulated as an integer linear programming model to minimize both network request blocking and crosstalk ratios simultaneously by considering core switching and inter-core crosstalk. To solve the model efficiently, we, therefore, design a joint routing and core coding scheme supporting core switching and propose a multiobjective evolutionary algorithm based on decomposition with adaptation and multi-strategy fusion (MOEA/D-AMSF), which integrates the new mechanisms of hybrid initial population generation, adaptive crossover, and double-layer and multi-point mutation in different iteration stages. These new mechanisms accelerate algorithm convergence and enhance solution diversity. Simulation results show that the proposed algorithm can obtain more dominated and diverse solutions compared with the existing multiobjective algorithm without considering core switching.

3D asymmetric expectation-maximization attention network for brain tumor segmentation.

Automatic brain tumor segmentation on MRI is a prerequisite to provide a quantitative and intuitive assistance for clinical diagnosis and treatment. Meanwhile, 3D deep neural network related brain tumor segmentation models have demonstrated considerable accuracy improvement over corresponding 2D methodologies. However, 3D brain tumor segmentation models generally suffer from high computation cost. Motivated by a recently proposed 3D dilated multi-fiber network (DMF-Net) architecture that pays more attention to reduction of computation cost, we present in this work a novel encoder-decoder neural network, ie a 3D asymmetric expectation-maximization attention network (AEMA-Net), to automatically segment brain tumors. We modify DMF-Net by introducing an asymmetric convolution block into a multi-fiber unit and a dilated multi-fiber unit to capture more powerful deep features for the brain tumor segmentation. In addition, AEMA-Net further incorporates an expectation-maximization attention (EMA) module into the DMF-Net by embedding the EMA block in the third stage of skip connection, which focuses on capturing the long-range dependence of context. We extensively evaluate AEMA-Net on three MRI brain tumor segmentation benchmarks of BraTS 2018, 2019 and 2020 datasets. Experimental results demonstrate that AEMA-Net outperforms both 3D U-Net and DMF-Net, and it achieves competitive performance compared with the state-of-the-art brain tumor segmentation methods.

Recurrent Multi-Fiber Network for 3D MRI Brain Tumor Segmentation

Automated brain tumor segmentation based on 3D magnetic resonance imaging (MRI) is critical to disease diagnosis. Moreover, robust and accurate achieving automatic extraction of brain tumor is a big challenge because of the inherent heterogeneity of the tumor structure. In this paper, we present an efficient semantic segmentation 3D recurrent multi-fiber network (RMFNet), which is based on encoder–decoder architecture to segment the brain tumor accurately. 3D RMFNet is applied in our paper to solve the problem of brain tumor segmentation, including a 3D recurrent unit and 3D multi-fiber unit. First of all, we propose that recurrent units segment brain tumors by connecting recurrent units and convolutional layers. This quality enhances the model’s ability to integrate contextual information and is of great significance to enhance the contextual information. Then, a 3D multi-fiber unit is added to the overall network to solve the high computational cost caused by the use of a 3D network architecture to capture local features. 3D RMFNet combines both advantages from a 3D recurrent unit and 3D multi-fiber unit. Extensive experiments on the Brain Tumor Segmentation (BraTS) 2018 challenge dataset show that our RMFNet remarkably outperforms state-of-the-art methods, and achieves average Dice scores of 89.62%, 83.65% and 78.72% for the whole tumor, tumor core and enhancing tumor, respectively. The experimental results prove our architecture to be an efficient tool for brain tumor segmentation accurately.

Modeling of human intervertebral disc annulus fibrosus with complex multi-fiber networks

Collagen fibers within the annulus fibrosus (AF) lamellae are unidirectionally aligned with alternating orientations between adjacent layers. AF constitutive models often combine two adjacent lamellae into a single equivalent layer containing two fiber networks with a crisscross pattern. Additionally, AF models overlook the inter‐lamellar matrix (ILM) as well as elastic fiber networks in between lamellae. We developed a nonhomogenous micromechanical model as well as two coarser homogenous hyperelastic and microplane models of the human AF, and compared their performances against measurements (tissue level uniaxial and biaxial tests as well as whole disc experiments) and seven published hyperelastic models. The micromechanical model had a realistic non-homogenous distribution of collagen fiber networks within each lamella and elastic fiber network in the ILM. For small matrix linear moduli (<0.2 MPa), the ILM showed substantial anisotropy (>10%) due to the elastic fiber network. However, at moduli >0.2 MPa, the effects of the elastic fiber network on differences in stress-strain responses at different directions disappeared (<10%). Variations in sample geometry and boundary conditions (due to uncertainty) markedly affected stress-strain responses of the tissue in uniaxial and biaxial tests (up to 16 times). In tissue level tests, therefore, simulations should represent testing conditions (e.g., boundary conditions, specimen geometry, preloads) as closely as possible. Stress/strain fields estimated from the single equivalent layer approach (conventional method) yielded different results from those predicted by the anatomically more accurate apparoach (i.e., layerwise). In addition, in a disc under a compressive force (symmetric loading), asymmetric stress-strain distributions were computed when using a layerwise simulation. Although all developed and selected published AF models predicted gross compression-displacement responses of the whole disc within the range of measured data, some showed excessively stiff or compliant responses under tissue-level uniaxial/biaxial tests. This study emphasizes, when constructing and validating constitutive models of AF, the importance of the proper simulation of individual lamellae as distinct layers, and testing parameters (sample geometric dimensions/loading/boundary conditions).

Modeling of Human Intervertebral Disc Annulus Fibrosus with Complex Multi-Fiber Networks

Collagen fibers within the annulus fibrosus (AF) lamellae are unidirectionally aligned with alternating orientations between adjacent layers. AF constitutive models often combine two adjacent lamellae into a single equivalent layer containing two fiber networks with a crisscross pattern. Additionally, AF models overlook the inter‐lamellar matrix (ILM) as well as elastic fiber networks in between lamellae. We developed a nonhomogenous micromechanical model as well as two coarser homogenous hyperelastic and microplane models of the human AF, and compared their performances against measurements (tissue level uniaxial and biaxial tests as well as whole disc experiments) and seven published hyperelastic models. The micromechanical model had a realistic non-homogenous distribution of collagen fiber networks within each lamella and elastic fiber network in the ILM. For small matrix linear moduli ( 10%) due to the elastic fiber network. However, at moduli >0.2 MPa, the effects of the elastic fiber network on differences in stress-strain responses at different directions disappeared (<10%). Variations in sample geometry and boundary conditions (due to uncertainty) markedly affected stress-strain responses of the tissue in uniaxial and biaxial tests (up to 16 times). In tissue level tests, therefore, simulations should represent testing conditions (e.g., boundary conditions, specimen geometry, preloads) as closely as possible. Stress/strain fields estimated from the single equivalent layer approach (conventional method) yielded different results from those predicted by the anatomically more accurate apparoach (i.e., layerwise). In addition, in a disc under a compressive force (symmetric loading), asymmetric stress-strain distributions were computed when using a layerwise simulation. Although all selected AF models predicted gross compression-displacement responses of the whole disc within the range of measured data, some showed excessively stiff or compliant responses under tissue-level uniaxial/biaxial tests. This study emphasizes, when constructing and validating constitutive models of AF, the importance of the proper simulation of individual lamellae as distinct layers, and testing parameters (sample geometric dimensions/loading/boundary conditions).

Real-Time Dense Semantic Labeling with Dual-Path Framework for High-Resolution Remote Sensing Image

Dense semantic labeling plays a pivotal role in high-resolution remote sensing image research. It provides pixel-level classification which is crucial in land cover mapping and urban planning. With the recent success of the convolutional neural network (CNN), accuracy has been greatly improved by previous works. However, most networks boost performance by involving too many parameters and computational overheads, which results in more inference time and hardware resources, while some attempts with light-weight networks do not achieve satisfactory results due to the insufficient feature extraction ability. In this work, we propose an efficient light-weight CNN based on dual-path architecture to address this issue. Our model utilizes three convolution layers as the spatial path to enhance the extraction of spatial information. Meanwhile, we develop the context path with the multi-fiber network (MFNet) followed by the pyramid pooling module (PPM) to obtain a sufficient receptive field. On top of these two paths, we adopt the channel attention block to refine the features from the context path and apply a feature fusion module to combine spatial information with context information. Moreover, a weighted cascade loss function is employed to enhance the learning procedure. With all these components, the performance can be significantly improved. Experiments on the Potsdam and Vaihingen datasets demonstrate that our network performs better than other light-weight networks, even some classic networks. Compared to the state-of-the-art U-Net, our model achieves higher accuracy on the two datasets with 2.5 times less network parameters and 22 times less computational floating point operations (FLOPs).

Deep learning improves automated rodent behavior recognition within a specific experimental setup

Automated observation and analysis of rodent behavior is important to facilitate research progress in neuroscience and pharmacology. Available automated systems lack adaptivity and can benefit from advances in AI. In this work we compare a state-of-the-art conventional rat behavior recognition (RBR) system to an advanced deep learning method and evaluate its performance within and across experimental setups. We show that using a multi-fiber network (MF-Net) in conjunction with data augmentation strategies within-setup dataset performance improves over the conventional RBR system. Two new methods for video augmentation were used: video cutout and dynamic illumination change. However, we also show that improvements do not transfer to videos in different experimental setups, for which we discuss possible causes and cures.

Battlefield Target Aggregation Behavior Recognition Model Based on Multi-Scale Feature Fusion

In this paper, our goal is to improve the recognition accuracy of battlefield target aggregation behavior while maintaining the low computational cost of spatio-temporal depth neural networks. To this end, we propose a novel 3D-CNN (3D Convolutional Neural Networks) model, which extends the idea of multi-scale feature fusion to the spatio-temporal domain, and enhances the feature extraction ability of the network by combining feature maps of different convolutional layers. In order to reduce the computational complexity of the network, we further improved the multi-fiber network, and finally established an architecture—3D convolution Two-Stream model based on multi-scale feature fusion. Extensive experimental results on the simulation data show that our network significantly boosts the efficiency of existing convolutional neural networks in the aggregation behavior recognition, achieving the most advanced performance on the dataset constructed in this paper.

A Span Power Management Scheme for Rapid Lightpath Provisioning and Releasing in Multi-Core Fiber Networks

The lightpath provisioning time or releasing time is adversely affected by the time that optical amplifiers require to adjust to a newly added or terminated signal power. This shortcoming is particularly true with multi-core erbium-doped amplifiers (EDFAs), as multi-core transient-suppressed EDFAs are unavailable at the current time. This paper proposes a fiber span power management scheme based on dummy wavelength signals that are used to shorten the lightpath provisioning and releasing times in multi-core fiber networks. With the shorter time of lightpath provisioning and releasing procedures, the total time that is required to reserve wavelengths in the system is decreased, which means that network resources are used more efficiently. As a result, the blocking performance and average waiting time in the system are improved. To evaluate the performance of the proposed scheme, this paper introduces both analytical model and simulation study. In the introduced model, the ratio of the number of activating and activated dummy wavelengths to the number of dummy wavelengths in each span is considered in the range between 0 and 1. The analysis reveals that the performance of the proposed scheme depends on $\alpha $ , which is the ratio of the number of dummy wavelengths to the number of dummy and lightpath wavelengths in each span, and there exists a point of $\alpha $ where the blocking probability becomes minimum. We further observe that the proposed scheme outperforms the conventional approaches in terms of blocking probability and average waiting time, as traffic loads increase. Finally, we provide the direction on how our introduced model can be considered for a network with multi-span routes.

CapEx advantages of multi-core fiber networks

We investigate capital expenditure (CapEx) advantages of multi-core fiber (MCF) networks by modeling and solving CapEx-minimized planning problem. Integer linear programming model is established, and numerical results are calculated and analyzed. We conduct the solving process under two kinds of traffic patterns of light traffic and heavy traffic. The influences of inter-core crosstalk on MCF and its multi-input multi-output (MIMO)-based crosstalk suppression are also evaluated. Numerical results show that when inter-core crosstalk in MCF is not considered, MCF networks have CapEx advantages under both given traffic patterns by using mixed MCF&SCF deployment strategy, despite the variation in MCF optical amplifier's price whose cost takes the largest share of the total network CapEx. However, when the inter-core crosstalk in MCF is taken into consideration, the costs of networks using MCF go higher than those of single-core fiber (SCF) networks. With the help of MIMO-based inter-core crosstalk suppression, the negative impact of inter-core crosstalk can be mitigated, and MCF can still show its CapEx advantages when the traffic load is heavy.

Dynamic lightpath establishment considering four-wave mixing in multifiber WDM networks

This paper proposes a dynamic lightpath establishment scheme considering four-wave mixing (FWM) in multifiber wavelength-division multiplexed (WDM) all-optical networks. The FWM is one of the most important physical impairments to be resolved in WDM networks because the FWM induces nonlinear inter-channel crosstalk and decays the performance of WDM networks. In WDM networks, data are transmitted via lightpaths. When the effect of FWM crosstalk is large, it is highly possible that data transmission fails even if lightpaths are correctly established. The proposed scheme aims to avoid not only the blocking of lightpath establishment but also the accumulation of FWM crosstalk by means of ingenious selection of routes, wavelengths, and fibers for lightpath establishment. In the proposed scheme, a route and a wavelength are selected for each lightpath based on wavelength availability and wavelength placement of established lightpaths. Furthermore, fibers on the route are selected based on estimated FWM power. In this paper, we show the effectiveness of the proposed scheme through simulation experiments.

PTES: A New Packet Transmission Technique in Bufferless Slotted OPS Networks

Optical packet contention is the major problem in optical packet switching (OPS) networks. In this paper, a software-based contention reduction scheme is proposed for all-optical multi-fiber slotted OPS networks, called packet transmission based on the scheduling of empty time-slots (PTES), suitable for overlaid star topology used in a metropolitan area with heterogeneous distances. In the scheduling procedure (performed in a distributed manner by each edge node of a star network) within a frame interval, some time-slots are scheduled as empty time-slots and the remaining time-slots are scheduled as non-empty. Then, an edge node must avoid sending its traffic in empty time-slots. Instead, non-empty time-slots can be used for traffic transmission. With respect to this scheduling, the variance of the number of non-empty time-slots that carry traffic from all edge nodes is minimized in the core node at each time-slot, thus reducing the traffic loss. Mathematical formulas are also provided to compute the traffic loss and delay under PTES. Performance evaluation results illustrate that PTES can reduce the number of collision events and traffic loss, especially at light and moderate traffic loads.

Impairment-aware Merit-based Scheduling in QoS-capable Multi-fiber OPS Networks

Impairment-aware Merit-based Scheduling in QoS-capable Multi-fiber OPS Networks

Power-Aware Routing and Wavelength Assignment in Multi-Fiber Optical Networks

This paper focuses on the energy consumption minimization problem of an optical transport network extending over a very wide area. In particular, the specific problem of power-aware routing and wavelength assignment (PA-RWA) is addressed considering a transparent multi-fiber optical network. An integer linear programming formulation is provided for the static lightpath establishment problem and a few heuristics are proposed to solve the problem in the case of dynamic lightpath establishment. To solve the routing problem we propose a novel algorithm named load based cost; it is based on a cost function that considers the load of each optical fiber to compute link weights. We also propose two new wavelength assignment algorithms: the first one is derived from the first fit heuristic whilst the second one is based on an innovative approach. It works like a least cost routing algorithm assigning a cost to each wavelength for each link in the path and then minimizes the total cost. Our proposal is compared with a number of already known RWA algorithms showing that it is able to reduce the power consumption of the network by about 20-30%, depending on the amount of traffic treated, with respect to state of the art algorithms with a difference of about 10% with respect to the lower bound. In order to provide a complete analysis of the feasibility of the proposed heuristics, the blocking probability is evaluated: the results show that, unlike the other power-aware algorithms here considered, our proposal shows a low impairment with respect to the least congested path-first fit alternative. Another important result regards the better performance of the proposed wavelength assignment algorithm with respect to first fit.

A framework for fiber delay-line buffers in packet-based asynchronous multifiber optical networks (PAMFONET)

A major challenge in packet-based optical networks is packet contention, which occurs when two or more packets are heading to the same output at the same time. To resolve contention in the optical domain, a fundamental approach is fiber delay-line (FDL) buffering, in which packets can be delayed for a fixed amount of time. In the literature, the performance of FDL buffering has been studied extensively. However, most existing works are based on an assumption that there is only one fiber per link in the network. In this paper, we address the architecture and performance of FDL buffers in packet-based asynchronous multifiber optical networks (PAMFONET), in which each link in the network may consist of multiple optical fibers. We propose a framework for FDL buffers in PAMFONET, in which we provide three essential architectures and corresponding packet scheduling policies. Extensive simulation results show that, with appropriate settings, the same number of FDLs can lead to better performance in multifiber networks than in single-fiber networks. Copyright © 2011 John Wiley & Sons, Ltd. (Here we note that such kind of multistage architectures are widely used in design and implementation of FDL buffers [14].

Homogeneous and Heterogeneous Subnetting for Constructing All-Optical Multifiber Networks

All-optical multifiber networks may require large and expensive optical switches (i.e., optical switches with many inputs/outputs). To tackle this problem, the existing approach adopts an individual node perspective and focuses on designing the internal node architectures that require smaller optical switches (i.e., optical switches with fewer inputs/outputs). In this paper, we adopt an entire network perspective and propose a logical subnetting approach to further reduce the switch size required. We use multiple logical subnets to compose a network, where a subnet has the same physical topology as but smaller dimensions than the network. In each subnet, each node has fewer incoming/outgoing fibers and hence it requires smaller optical switches. A lightpath can be set up through any one of the available subnets. We propose two subnetting methods: (i) homogeneous subnetting in which all subnets are identical and (ii) heterogeneous subnetting in which different subnets may adopt different node architectures and dimensions. Logical subnetting has three advantages: (i) the resulting network requires significantly smaller optical switches, while its blocking probability can be nearly the same, (ii) logical subnetting can complement any existing node architectures to integrate their respective advantages and further reduce the switch size required, and (iii) an existing network can easily be scaled up by adding additional subnets without modifying the existing ones.

Multicast Routing and Wavelength Assignment with Shared Protection in Multi-Fiber WDM Mesh Networks: Optimal and Heuristic Solutions

While the problem of multicast routing and wavelength assignment (MC-RWA) in optical wavelength division multiplexing (WDM) networks has been investigated, relatively few researchers have considered network survivability for multicasting. This paper provides an optimization framework to solve the MC-RWA problem in a multi-fiber WDM network that can recover from a single-link failure with shared protection. Using the light-tree (LT) concept to support multicast sessions, we consider two protection strategies that try to reduce service disruptions after a link failure. The first strategy, called light-tree reconfiguration (LTR) protection, computes a new multicast LT for each session affected by the failure. The second strategy, called optical branch reconfiguration (OBR) protection, tries to restore a logical connection between two adjacent multicast members disconnected by the failure. To solve the MC-RWA problem optimally, we propose an integer linear programming (ILP) formulation that minimizes the total number of fibers required for both working and backup traffic. The ILP formulation takes into account joint routing of working and backup traffic, the wavelength continuity constraint, and the limited splitting degree of multicast-capable optical cross-connects (MC-OXCs). After showing some numerical results for optimal solutions, we propose heuristic algorithms that reduce the computational complexity and make the problem solvable for large networks. Numerical results suggest that the proposed heuristic yields efficient solutions compared to optimal solutions obtained from exact optimization.