Joint Minimization Research Articles

Support Matrix Machine via Joint l2,1 and Nuclear Norm Minimization Under Matrix Completion Framework for Classification of Corrupted Data.

Traditional support vector machines (SVMs) are fragile in the presence of outliers; even a single corrupt data point can arbitrarily alter the quality of the approximation. If even a small fraction of columns is corrupted, then classification performance will inevitably deteriorate. This article considers the problem of high-dimensional data classification, where a number of the columns are arbitrarily corrupted. An efficient Support Matrix Machine that simultaneously performs matrix Recovery (SSMRe) is proposed, i.e. feature selection and classification through joint minimization of l2,1 (the nuclear norm of L ). The data are assumed to consist of a low-rank clean matrix plus a sparse noisy matrix. SSMRe works under incoherence and ambiguity conditions and is able to recover an intrinsic matrix of higher rank in the presence of data densely corrupted. The objective function is a spectral extension of the conventional elastic net; it combines the property of matrix recovery along with low rank and joint sparsity to deal with complex high-dimensional noisy data. Furthermore, SSMRe leverages structural information, as well as the intrinsic structure of data, avoiding the inevitable upper bound. Experimental results on different real-time applications, supported by the theoretical analysis and statistical testing, show significant gain for BCI, face recognition, and person identification datasets, especially in the presence of outliers, while preserving a reasonable number of support vectors.

Multi-objective branch-and-bound for the design-for-control of water distribution networks with global bounds

This study investigates a design-for-control (DfC) problem formulation for the joint minimization of pressure-induced leakage, maximization of resilience, and minimization of cost in water distribution networks (WDN). The DfC problem, which consists in simultaneously installing new valves and/or pipes and optimizing valve control settings, results in a challenging optimization problem belonging to the class of non-convex multi-objective mixed-integer non-linear programs (MOMINLP). Due to their complex mathematical structure, multi-objective WDN design-for-control problems have previously been solved using general-purpose evolutionary algorithms or local deterministic methods, which do not provide guarantees on the quality of the returned solutions. While branch-and-bound (BB) frameworks have been proposed to approximate the Pareto fronts of MOMINLPs with global bounds, they rely on the availability of attainable solutions which, for WDN design-for-control problems, can be hard to identify. Moreover, in the absence of general-purpose solvers, the performance of multi-objective BB implementations depends, for a given application, on the choice of adequate branching and lower bounding strategies. In this study, we investigate a multi-objective BB algorithm based on tailored branching, lower bounding and additional upper bounding strategies to efficiently approximate the Pareto front of WDN design-for-control problems with bounds of ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon$$\\end{document}-non-dominance. The proposed algorithm is applied to the optimal DfC of two case study networks and is shown to outperform alternative solution methods.

An Experimental Research of the Algorithm for Extracting of a Boolean Function Subsystems for Joint Multilevel Optimization

The results of an experimental comparison of programs for technologically independent minimization of complexity of multilevel representations of systems of fully defined functions based on the Shannon expansion are described. The main attention is paid to the effectiveness of using, when synthesizing logical circuits, a program that implements an algorithm for solving the problem of extracting from a system of functions such subsystems for which it is advisable to carry out joint minimization of multi-level representations of subsystems in the form of Binary Decision Diagrams, called BDD-representations, and in the form of Boolean net. The complexity of the representation is estimated by the total number of literals of Boolean variables in a set of interrelated logical equations that define a system of Boolean functions. After extracting the subsystems and their joint minimization, the synthesis of logic circuits is carried out in the design library of custom digital CMOS VLSIs, the results are compared in terms of chip area and speed (time delay) on a stream of 39 industrial examples of circuits. It was found that for 20 examples, the subsystem selection algorithm allows one to obtain better solutions than joint or separate minimization of multi-level representations based on Shannon expansion (13 examples). The three best solutions are obtained by applying the well-known Espresso program for minimizing functions in the DNF class, and the three solutions are obtained by the synthesizer using the original (non-optimized) matrix representations of DNF systems of Boolean functions.

Technology independent optimization when implementing sparse systems of disjunctive normal forms of Boolean functions in ASIC

Objectives. The problem of choosing the best methods and programs for circuit implementation as part of digital ASIC (Application-Specific Integrated Circuit) sparse systems of disjunctive normal forms (DNF) of completely defined Boolean functions is considered. For matrix forms of sparse DNF systems, the ternary matrix specifying elementary conjunctions contains a large proportion of undefined values corresponding to missing literals of Boolean input variables, and the Boolean matrix specifying the occurrences of conjunctions in DNF functions contains a large proportion of zero values.Methods. It is proposed to investigate various methods of technologically independent logical optimization performed at the first stage of logical synthesis: joint minimization of systems of functions in the DNF class, separate and joint minimization in classes of multilevel representations in the form of Boolean networks and BDD representations using mutually inverse cofactors, as well as the division of a system of functions into subsystems with a limited number of input variables and the method of block cover of DNF systems, focused on minimizing the total area of the blocks forming the cover.Results. When implementing sparse DNF systems of Boolean functions in ASIC, along with traditional methods of joint minimization of systems of functions in the DNF class, methods for optimizing multilevel representations of Boolean function systems based on Shannon expansions can be used for technologically independent optimization, while separate minimization and joint minimization of the entire system as a whole turn out to be less effective compared with block partitions and coatings of the DNF system and subsequent minimization of multilevel representations. Schemes obtained as a result of synthesis using minimized representations of Boolean networks often have a smaller area than schemes obtained using minimized BDD representations.Conclusion. For the design of digital ASIC, the effectiveness of combined approach is shown, when initially the block coverage programs of the DNF system is used, followed by the use of programs to minimize multilevel block representations in the form of Boolean networks minimized based on Shannon expansion.

Masticatory Muscles Activation and TMJ Space During Asymmetrically Loaded Jaw Closing

Masticatory muscle activation and temporomandibular joint (TMJ) load generated during asymmetrically loaded jaw closing are largely unknown. Two different strategies were developed to explain how the central nervous system (CNS) generates muscle activation patterns during motion: minimization of joint load (MJL) vs. minimization of muscle effort (MME). The aim of the present study was to investigate, experimentally, the neuromuscular strategy selected by the CNS to coordinate jaw closing in reaction to the application of an external asymmetric load. Masticatory muscle activation was measured with electromyography (EMG) and the minimum intra-articular distance (MID) was assessed by dynamic stereometry to infer joint loading. Ten healthy subjects performed jaw-closing movements against an asymmetric mandibular load set from 0.0 to 2.0 kg in 0.5-kg steps. Recordings were analyzed by exploratory and graphical statistical tools. Moreover, the observed differences in MID and EMG among the various mandibular loads were tested using non-parametric tests for repeated measures data. The ipsilateral-contralateral differences in MID and EMG of the anterior temporalis showed a significant increase (p < 0.001, p = 0.01) with increasing asymmetrical load with both joints being most heavily loaded at 1 kg. EMG signals of the masseter did not change significantly with increasing load. This study is the first to have analyzed the changes in the TMJ intra-articular space during asymmetrically loaded jaw-closing movements, not only three dimensionally and dynamically, but also combined with EMG. Asymmetrical load affected the TMJ space and masticatory muscle activation patterns, primarily resulting in an increased activation of the anterior temporalis muscle. This might suggest the involvement of a control mechanism to protect the joints from overloading. However, the results do not fully support the hypothesis of MJL nor the MME strategy.

Joint and Separate Minimization of Multilevel Representations of Boolean Function Systems

The results of experimental studies of the effectiveness of programs for minimizing multilevel representations of systems of Boolean functions performed during the synthesis of combinational circuits in the design library of custom CMOS VLSI are presented. The efficiency of joint and separate minimization programs using Shannon expansions for constructing multilevel representations of systems of fully defined Boolean functions in the form of interconnected systems of logical equations — complete or abbreviated formulas of Shannon expansion or formulas corresponding to Boolean networks is investigated. A comparison is made with the results of experiments performed for various types of joint minimization only. A comparison is also made with the results of solutions obtained by the program of joint and separate minimization of Boolean function systems in the DNF class. It is shown that the use of joint minimization of multi-level representations makes it possible to obtain circuits of a smaller area more often, and the use of a separate one — circuits with a lower delay.

Deadline-Constrained Multi-Agent Collaborative Transmission for Delay-Sensitive Applications

Delay-sensitive applications impose the strict deadline-constrained latency requirement for end-to-end transmission. However, due to the high dynamics of link status and the limited network resources, it is still challenging to ensure deterministic end-to-end latency for deadline-constrained flows. To this end, we propose a deadline-constrained multi-agent collaborative transmission mechanism (DMCT). Specially, DMCT is featured by combining dynamic routing and packet active dropping control to avoid additional end-to-end latency. Firstly, we design a specific packet structure to detect network status and aware the deadline of each flow. Secondly, to enhance the precision of routing decision, we further formulate deadline-constrained flow scheduling as a joint minimization problem that considers the deadline of flows, queuing delay, and network status. Then, we propose a multi-agent collaborative routing algorithm to find the solution to the joint minimization problem. Finally, we propose a local-agent deadline-constrained active queue management algorithm for packet active dropping control and routing adjustment. Simulation results show that the proposed DMCT outperforms the state-of-the-art solutions, e.g., graph convolutional network-based deep reinforcement learning (GCNL) and delay-based shortest path first (D-SPF), in terms of one-way round-trip time, drop rate, and queue length.

Downlink Multi-IRS Aided NOMA System With Second-Order Reflection

The performance of non-orthogonal multiple access (NOMA) system can be enhanced by the incorporation of intelligent reflecting surface (IRS), which has the capability of reconfiguring each user’s channel condition according to the demands. In this letter, we aim to design a transmission scheme with low power consumption for downlink multi-IRS assisted NOMA system with the consideration of second-order reflection. To this end, a joint transmit power and phase shift optimization problem is formulated. By leveraging the relationship between the phase shifts and each user’s required transmit power, the joint minimization problem is simplified as a pure phase shift optimization problem. To further address the transformed non-convex problem, a successive phase-rotation method is proposed to determine the phase shifts sequentially. Simulation results show that the proposed scheme performs better than extensive benchmarking schemes in terms of total transmit power.

EmoKbGAN: Emotion controlled response generation using Generative Adversarial Network for knowledge grounded conversation.

Neural open-domain dialogue systems often fail to engage humans in long-term interactions on popular topics such as sports, politics, fashion, and entertainment. However, to have more socially engaging conversations, we need to formulate strategies that consider emotion, relevant-facts, and user behaviour in multi-turn conversations. Establishing such engaging conversations using maximum likelihood estimation (MLE) based approaches often suffer from the problem of exposure bias. Since MLE loss evaluates the sentences at the word level, we focus on sentence-level judgment for our training purposes. In this paper, we present a method named EmoKbGAN for automatic response generation that makes use of the Generative Adversarial Network (GAN) in multiple-discriminator settings involving joint minimization of the losses provided by each attribute specific discriminator model (knowledge and emotion discriminator). Experimental results on two bechmark datasets i.e the Topical Chat and Document Grounded Conversation dataset yield that our proposed method significantly improves the overall performance over the baseline models in terms of both automated and human evaluation metrics, asserting that the model can generate fluent sentences with better control over emotion and content quality.

Small steps for mankind: Modeling the emergence of cumulative culture from joint active inference communication.

Although the increase in the use of dynamical modeling in the literature on cultural evolution makes current models more mathematically sophisticated, these models have yet to be tested or validated. This paper provides a testable deep active inference formulation of social behavior and accompanying simulations of cumulative culture in two steps: First, we cast cultural transmission as a bi-directional process of communication that induces a generalized synchrony (operationalized as a particular convergence) between the belief states of interlocutors. Second, we cast social or cultural exchange as a process of active inference by equipping agents with the choice of who to engage in communication with. This induces trade-offs between confirmation of current beliefs and exploration of the social environment. We find that cumulative culture emerges from belief updating (i.e., active inference and learning) in the form of a joint minimization of uncertainty. The emergent cultural equilibria are characterized by a segregation into groups, whose belief systems are actively sustained by selective, uncertainty minimizing, dyadic exchanges. The nature of these equilibria depends sensitively on the precision afforded by various probabilistic mappings in each individual's generative model of their encultured niche.

Hardware Implementation of Code Converters Designed to Reduce the Length of Binary Encoded Words

The problem of synthesis of combinational circuits of code converters designed to reduce the length of words from a given set of encoded binary words is considered. The encoding assumes that different binary words will be encoded by different binary codes of shorter length. Code converters of this type are designed to reduce the length of binary words transmitted in digital systems over data buses when the bit depth of the transmitted words exceeds the bit depth of the data bus. For example, 18-bit or 17-bit words need to be transmitted over a 16-bit data bus. Each such word can be transmitted in two cycles of operation of a digital system, however, this approach reduces the overall performance of the system. One of the approaches to solve such problems is the development of combinational circuits that convert long binary encoded words into shorter ones. The proposed methods for solving the problem of synthesizing circuits of code converters are based on the compilation and logical minimization of such forms of systems of incompletely specified Boolean functions as disjunc­tive normal forms (DNF) and binary decision diagrams (BDD). Using BDD to minimize representations of k-valued functions that depend on Boolean variables is also proposed. Technologically independent logical minimization of functional descriptions of the designed code converters is proposed to be performed by programs for minimizing systems of Boolean functions in the DNF class and programs for joint minimization of BDD representations of systems of completely specified Boolean functions. Minimization of functional descriptions is aimed at reducing the hardware complexity of combinational circuits in the basis of library elements or programmable FPGA elements implementing code converters of the class in question.

Unsupervised moving object segmentation using background subtraction and optimal adversarial noise sample search

Moving Objects Segmentation (MOS) is a fundamental task in many computer vision applications such as human activity analysis, visual object tracking, content based video search, traffic monitoring, surveillance, and security. MOS becomes challenging due to abrupt illumination variations, dynamic backgrounds, camouflage and scenes with bootstrapping. To address these challenges we propose a MOS algorithm exploiting multiple adversarial regularizations including conventional as well as least squares losses. More specifically, our model is trained on scene background images with the help of cross-entropy loss, least squares adversarial loss and ℓ1 loss in image space working jointly to learn the dynamic background changes. During testing, our proposed method aims to generate test image background scenes by searching optimal noise samples using joint minimization of ℓ1 loss in image space, ℓ1 loss in feature space, and discriminator least squares loss. These loss functions force the generator to synthesize dynamic backgrounds similar to the test sequences which upon subtraction results in moving objects segmentation. Experimental evaluations on five benchmark datasets have shown excellent performance of the proposed algorithm compared to the twenty one existing state-of-the-art methods.

Simultaneous minimization of side‐band power and PAPR in OFDM based cognitive radio without additional bandwidth requirement for sending SI

AbstractCognitive radio (CR) incorporating orthogonal frequency division multiplexing (OFDM) is an intelligent spectrum sharing technique that acquires high data rate in frequency selective fading environment. OFDM has been successfully used for 4G and specific version of OFDM is being considered as the multiple access technology for 5G as well. However OFDM signal is more likely to have high peak‐to‐average power ratio (PAPR). Similarly, the sideband power of secondary or temporary users (SU) in CR can lead to interference to the licensed or primary users of the neighboring bands. In this work, an improved technique for the joint minimization of sideband power and PAPR using Zadoff‐Chu (ZC) sequence is proposed for CR based on OFDM technology. Furthermore, we propose a detection algorithm based on a binary hypothesis testing problem to recover the chosen ZC sequence at the receiver side eliminating the requirement of side information (SI) transmission. Simulation studies of the proposed method exhibits the efficiency of the concurrent reduction of PAPR and sideband power along with a huge bandwidth saving by the omission of the SI transmission.

Experimental comparison of the effectiveness of programs for minimizing systems of Boolean functions in the class of disjunctive normal forms

Objectives. Methods, algorithms and programs for solving problems of minimizing the DNF representations of Boolean functions are widely used in the design of digital systems to reduce the complexity (crystal area) of functional combinational blocks of digital systems placed into digital VLSI.The objective of the work is experimental comparison of domestic programs for minimizing Boolean functions in the DNF class included in the FLC-2 with two well-known foreign freely distributed programs for minimizing DNF known as Espresso IIC and ABC.Methods. Four sets sample of input data were used to compare the programs – there are widely known examples on which the effectiveness of the Espresso IIC program was tested and two sets of industrial examples from the practice of designing the logic circuits. Algorithms and programs for parallelization of calculations when separate functions of minimizing have been developed. Software tools for the application of joint minimization programs with separate minimization of functions are proposed.Results. The areas of preferred use and the execution time of programs for the source systems of functions (for minimization) characterized by large parameter values of dozens of arguments and functions, tens of thousands of elementary conjunctions are revealed. The efficiency of application of minimization programs for various forms of input data assignment is investigated – DNF, orthogonalized DNF, BDD (Binary Decision Diagrams) representations for systems of functions, truth tables and perfect DNF systems.Conclusion. The experimental results show the effectiveness of parallel programs – reducing the calculation time and increasing the dimensions of solved problems of separate minimization of Boolean function systems.

PAPR Reduction in MIMO-OFDM via Power Efficient Transmit Waveform Shaping

In this paper we revisit the long standing problem of peak-to-average power ratio minimization in MIMO-OFDM systems, with a new angle of approach on a well-known scheme. Utilizing the principles of tone reservation, we place dummy symbols, i.e., complex coefficients, on unused space-frequency resources with the aim to jointly minimize the transmit signal PAPR and the self-power consumption of the dummy symbols. This joint minimization is solved using three different proposed algorithms exhibiting varying degrees of computational complexity and PAPR reduction performance. Our proposed framework utilizes the strict PAPR expression, i.e., we take into account the average transmit power of the antenna, to simultaneously reduce the PAPR on all antennas while keeping the self-power consumption of the scheme minimal. Our simulation results show that this optimization objective provides better worst-case PAPR reduction and dummy symbol power consumption performance compared to the peak power minimization objective widely utilized in the tone reservation literature. Finally, we propose a novel take on a well-known block-diagonalization algorithm by exploiting knowledge on dummy symbol allocations, resulting in high-gain data streams in downlink transmission.

Prediction of post transarterial chemoembolization MR images of hepatocellular carcinoma using spatio-temporal graph convolutional networks.

Magnetic resonance imaging (MRI) plays a critical role in the planning and monitoring of hepatocellular carcinomas (HCC) treated with locoregional therapies, in order to assess disease progression or recurrence. Dynamic contrast-enhanced (DCE)-MRI sequences offer temporal data on tumor enhancement characteristics which has strong prognostic value. Yet, predicting follow-up DCE-MR images from which tumor enhancement and viability can be measured, before treatment of HCC actually begins, remains an unsolved problem given the complexity of spatial and temporal information. We propose an approach to predict future DCE-MRI examinations following transarterial chemoembolization (TACE) by learning the spatio-temporal features related to HCC response from pre-TACE images. A novel Spatial-Temporal Discriminant Graph Neural Network (STDGNN) based on graph convolutional networks is presented. First, embeddings of viable, equivocal and non-viable HCCs are separated within a joint low-dimensional latent space, which is created using a discriminant neural network representing tumor-specific features. Spatial tumoral features from independent MRI volumes are then extracted with a structural branch, while dynamic features are extracted from the multi-phase sequence with a separate temporal branch. The model extracts spatio-temporal features by a joint minimization of the network branches. At testing, a pre-TACE diagnostic DCE-MRI is embedded on the discriminant spatio-temporal latent space, which is then translated to the follow-up domain space, thus allowing to predict the post-TACE DCE-MRI describing HCC treatment response. A dataset of 366 HCC's from liver cancer patients was used to train and test the model using DCE-MRI examinations with associated pathological outcomes, with the spatio-temporal framework yielding 93.5% classification accuracy in response identification, and generating follow-up images yielding insignificant differences in perfusion parameters compared to ground-truth post-TACE examinations.

Евристичний метод для bitsliced подання випадково згенерованих 88 криптографічних S-Box

The article is devoted to the issues of increasing the security and efficiency of software implementation for the symmetric block ciphers. For the implementation of cryptoalgorithms on low-end CPUs (8/16/32-bit microcontrollers), it is important to provide increased resistance to power consumption analysis attacks. With regard to the implementation of ciphers on high-end CPUs (x86, ARM Cortex-A), it is important to eliminate the vulnerability primarily to timing and cache attacks. The authors used a bitslice approach to securely implement block ciphers, which has potential advantages such as high speed and low computing resources. However, the known bitsliced methods have a significant limitation, since they work with deterministic S-Boxes or arbitrary S-Boxes of smaller sizes. The paper proposes a new heuristic method for bitsliced representation of cryptographic 8×8 S-Boxes containing randomly generated values. These values defy description using algebraic expressions. The method is based on the decomposition of the truth table, which describes the S-Box, into two parts. One part of the table forms logical masks, and the other is split into bit vectors. To find a logical description of these vectors an exhaustive search is used. After finding the description of all vectors, these two parts of the table are combined into one using logical operations. The use of this method oriented on software implementation in the logical basis {AND, OR, XOR, NOT} ensures the minimization of arbitrary 8×8 S-Boxes. The proposed method can be implemented using standard logical instructions on any 8/16/32/64-bit processors. It is also possible to use logical SIMD instructions from the SSE, AVX, AVX-512 extensions for x86-64 processors, which provides high performance due to the use of long registers. The corresponding software has been developed that implements the method of searching for bitsliced representations of a given S-Box, and also automatically generates C++ code for it based on SSE, AVX and AVX-512 instructions. The effectiveness of the method on the S-Box of known block ciphers, in particular the Ukrainian encryption standard "Kalyna", has been investigated. It was found that the developed algorithm requires almost half as many gates for the bitsliced description of an arbitrary S-Box than the best of known algorithm (370 gates versus 680, respectively). For ciphers that use two or four S-Box tables, joint minimization can yield up to 330 or 300 gates per table, respectively. Keywords: bitslicing; S-Box; logical minimization; SIMD; x86-64 CPU; software implementation; block ciphers.

Hierarchical feature selection with multi-granularity clustering structure

Hierarchical feature selection addresses the issues caused by the presence of high-dimensional features in multi-category classification systems with hierarchical structures. Granular calculations are made to analyze the hierarchical relationships among categories when selecting the optimal feature subset. However, semantic hierarchy-based feature selection methods are prone to the semantic gap problem, which affects classification accuracy. In this paper, we propose a hierarchical feature selection method with a multi-granularity clustering structure that can effectively alleviate the semantic gap problem. Firstly, a hierarchical structure is constructed via bottom-up multi-granularity clustering based on feature similarities rather than semantic categories. This clustering hierarchy is conducive to solving semantic gap problems in the existing hierarchy. Secondly, the optimal feature subset is selected using the ℓ1,2-norms in each hierarchy’s granularity layer. This joint minimization approach can retain both the granularity layers’ shared features and granularity-specific features. Finally, we execute hierarchical classification according to the granular structure in a coarse to fine sequence. Extensive experiments demonstrate that the proposed method outperforms several state-of-the-art hierarchical feature selection approaches.

TSingNet: Scale-aware and context-rich feature learning for traffic sign detection and recognition in the wild

Traffic sign detection and recognition in the wild is a challenging task. Existing techniques are often incapable of detecting small or occluded traffic signs because of the scale variation and context loss, which causes semantic gaps between multiple scales. We propose a new traffic sign detection network (TSingNet), which learns scale-aware and context-rich features to effectively detect and recognize small and occluded traffic signs in the wild. Specifically, TSingNet first constructs an attention-driven bilateral feature pyramid network, which draws on both bottom-up and top-down subnets to dually circulate low-, mid-, and high-level foreground semantics in scale self-attention learning. This is to learn scale-aware foreground features and thus narrow down the semantic gaps between multiple scales. An adaptive receptive field fusion block with variable dilation rates is then introduced to exploit context-rich representation and suppress the influence of occlusion at each scale. TSingNet is end-to-end trainable by joint minimization of the scale-aware loss and multi-branch fusion losses, this adds a few parameters but significantly improves the detection performance. In extensive experiments with three challenging traffic sign datasets (TT100K, STSD and DFG), TSingNet outperformed state-of-the-art methods for traffic sign detection and recognition in the wild.

Joint Minimization of Spectrum and Power in Impairment-Aware Elastic Optical Networks

Flexible-grid elastic optical networks (EONs) are widely considered as the future of next generation optical transport networks. Depleting spectral resources and increasing power consumption are two critical bottlenecks of EONs. In this paper, we propose a novel impairment-aware resource allocation scheme that jointly minimizes bandwidth waste and power consumption of EONs. The proposed scheme is presented in the form of an analytical optimization for small-sized networks. A low-complexity heuristic is then proposed for large networks. Numerical results show that by appropriately assigning the route, modulation format, and carrier frequency to each connection request, the proposed scheme significantly increases spectral efficiency and reduces power consumption in networks that handle varying traffic volumes.