Linear Sum Assignment Research Articles

Multi-Channel Cooperative Spectrum Sensing and Scheduling for Cognitive IoT Networks

This paper presents a novel multi-channel cooperative spectrum sensing and scheduling (MC$_2$S$_3$) framework for spectrum and energy harvesting cognitive Internet of Things (IoT) networks. We address the challenge of maximizing network throughput by formulating a combinatorial problem that jointly optimizes the sensing scheduling of primary channels (PCs), the assignment of IoT devices for sensing scheduled PCs, and the clustering and allocation of IoT nodes to efficiently use discovered idle PCs; subject to spectrum utilization and collision avoidance constraints. Recognizing the inherent complexity of the underlying NP-hard mixed-integer non-linear programming (MINLP) problem, we propose a decomposition strategy that decouples the master problem into PC exploration and exploitation sub-problems. In the exploration phase, we derive closed-form solutions for optimal sensing durations and detection thresholds that satisfies spectrum utilization and collision avoidance constraints, which are then used to develop a priority metric to rank PCs. The proposed PC ranking informs a sequential PC scheduling and IoT sensing assignment approach that exploits a linear bottleneck assignment (LBA) strategy, proceeding until further scheduling does not enhance network utility. For the exploitation phase, we leverage a non-orthogonal multiple access (NOMA) strategy to multiplex multiple IoT nodes on a single PC, employing an iterative linear sum assignment (LSA) method for efficient allocation to maximize utilization of idle PCs. Numerical results validate the efficacy of our proposed methodologies, reaching an accuracy of approximately 99% in the order of milliseconds, significantly outperforming time complexity of brute-force benchmarks.

A Graph-Based Neural Approach to Linear Sum Assignment Problems.

Linear assignment problems are well-known combinatorial optimization problems involving domains such as logistics, robotics and telecommunications. In general, obtaining an optimal solution to such problems is computationally infeasible even in small settings, so heuristic algorithms are often used to find near-optimal solutions. In order to attain the right assignment permutation, this study investigates a general-purpose learning strategy that uses a bipartite graph to describe the problem structure and a message passing Graph Neural Network (GNN) model to learn the correct mapping. Comparing the proposed structure with two existing DNN solutions, simulation results show that the proposed approach significantly improves classification accuracy, proving to be very efficient in terms of processing time and memory requirements, due to its inherent parameter sharing capability. Among the many practical uses that require solving allocation problems in everyday scenarios, we decided to apply the proposed approach to address the scheduling of electric smart meters access within an electricity distribution smart grid infrastructure, since near-real-time energy monitoring is a key element of the green transition that has become increasingly important in recent times. The results obtained show that the proposed graph-based solver, although sub-optimal, exhibits the highest scalability, compared with other state-of-the-art heuristic approaches. To foster the reproducibility of the results, we made the code available at https://github.com/aircarlo/GNN_LSAP.

How to fairly and efficiently assign tasks in individually rational agents’ coalitions? Models and fairness measures

An individually rational agent will participate in a multi-agent coalition if the participation, given available information and knowledge, brings a payoff that is at least as high as the one achieved by not participating. Since agents? performance and skills may vary from task to task, the decisions about individual agent-task assignment will determine the overall performance of the coalition. Maximising the efficiency of the one-on-one assignment of tasks to agents corresponds to the conventional linear sum assignment problem, which considers efficiency as the sum of the costs or benefits of individual agent-task assignments obtained by the coalition as a whole. This approach may be unfair since it does not explicitly consider fairness and, thus, is unsuitable for individually rational agents? coalitions. In this paper, we propose two new assignment models that balance efficiency and fairness in task assignment and study the utilitarian, egalitarian, and Nash social welfare for task assignment in individually rational agents? coalitions. Since fairness is a relatively abstract term that can be difficult to quantify, we propose three new fairness measures based on equity and equality and use them to compare the newly proposed models. Through functional examples, we show that a reasonable trade-off between efficiency and fairness in task assignment is possible through the use of the proposed models.

HDT network: A high‐resolution range profile multi‐target detection and tracking method based on neural network

AbstractIn radar target detection and tracking tasks, the detection algorithm and data association algorithm are the primary technologies. The accuracy of detection, stability of tracking and processing speed are the key points to accomplishing effective high‐resolution range profile (HRRP) multi‐target tracking (MTT). Classic HRRP target tracking algorithms conduct the detection by extracting handcraft features and conduct tracking based on the data association algorithm. With the development of neural network methods, deep learning methods have been widely applied in target detection and tracking. An HRRP detection and tracking (HDT) network based on neural networks is proposed, which includes three steps: Firstly, the HRRP signal is processed by a convolutional neural network detector to extract the feature of the origin signal and generate the detection measurement. Secondly, a predicted measurement is generated by a Kalman filter, which estimates the current state of the target based on its previous states and the detection measurement. Finally, the ReID network calculates the cosine similarity between the tracks and measurements to associate them and a linear sum assignment operation is used to match the tracks and measurements. By using the proposed algorithm, the HDT network is capable of detecting and tracking multiple targets in complex cluttered environments with high accuracy. Experimental results on an HRRP dataset collected by a moving radar platform show the outstanding performance of the HDT network, including detection accuracy, track integrity and real‐time MTT.

Bayesian Federated Neural Matching That Completes Full Information

Federated learning is a contemporary machine learning paradigm where locally trained models are distilled into a global model. Due to the intrinsic permutation invariance of neural networks, Probabilistic Federated Neural Matching (PFNM) employs a Bayesian nonparametric framework in the generation process of local neurons, and then creates a linear sum assignment formulation in each alternative optimization iteration. But according to our theoretical analysis, the optimization iteration in PFNM omits global information from existing. In this study, we propose a novel approach that overcomes this flaw by introducing a Kullback-Leibler divergence penalty at each iteration. The effectiveness of our approach is demonstrated by experiments on both image classification and semantic segmentation tasks.

Experimental Evaluation of AGV Dispatching Methods in an Agent-Based Simulation Environment and a Digital Twin

A critical part of Automated Material Handling Systems (AMHS) is the task allocation and dispatching strategy employed. In order to better understand and investigate this component, we here present an extensive experimental evaluation of three different approaches with randomly generated, as well as custom designed, environment configurations. While previous studies typically focused on use cases based on highly constrained navigation capabilities (e.g., overhead hoist transport systems), our evaluation is built around highly mobile, free-ranging vehicles, i.e., Autonomous Mobile Robots (AMR) that are gaining popularity in a broad range of applications. Consequently, our experiments are conducted using a microscopic agent-based simulation, instead of the more common discrete-event simulation model. Dispatching methods often are built around the assumption of the asynchronous evaluation of an event-based model, i.e., vehicles trigger a cascade of individual dispatching decisions, e.g., when reaching intersections. We find that this does not translate very well to a fleet of highly mobile systems that can change direction at any time. With this in mind, we present formulations of well known dispatching approaches that are better suited for a synchronous evaluation of the dispatching decisions. The formulations are based on the Stable Marriage Problem (SMP) and the Linear Sum Assignment Problem (LSAP). We use matching and assignment algorithms to compute the actual dispatching decisions. The selected algorithms are evaluated in a multi-agent simulation environment. To integrate a centralised fleet management, a digital twin concept is proposed and implemented. By this approach, the fleet management is independent of the implementation of the specific agents, allowing to quickly adapt to other simulation-based or real application scenarios. For the experimental evaluation, two new performance measures related to the efficiency of a material handling system are proposed, Travel Efficiency and Throughput Effort. The experimental evaluation indicates that reassignment mechanisms in the dispatching method can help to increase the overall efficiency of the fleet. We did not find significant differences in absolute performance in terms of throughput rate. Additionally, the difference in performance between SMP- and LSAP-based dispatching with reassignment seems negligible. We conclude with a discussion, where we consider potential confounding factors and relate the findings to previously reported results found in the literature.

Fast Multi-UAV Path Planning for Optimal Area Coverage in Aerial Sensing Applications.

This paper deals with the problems and the solutions of fast coverage path planning (CPP) for multiple UAVs. Through this research, the problem is solved and analyzed with both a software framework and algorithm. The implemented algorithm generates a back-and-forth path based on the onboard sensor footprint. In addition, three methods are proposed for the individual path assignment: simple bin packing trajectory planner (SIMPLE-BINPAT); bin packing trajectory planner (BINPAT); and Powell optimized bin packing trajectory planner (POWELL-BINPAT). The three methods use heuristic algorithms, linear sum assignment, and minimization techniques to optimize the planning task. Furthermore, this approach is implemented with applicable software to be easily used by first responders such as police and firefighters. In addition, simulation and real-world experiments were performed using UAVs with RGB and thermal cameras. The results show that POWELL-BINPAT generates optimal UAV paths to complete the entire mission in minimum time. Furthermore, the computation time for the trajectory generation task decreases compared to other techniques in the literature. This research is part of a real project funded by the H2020 FASTER Project, with grant ID: 833507.

Upper Bounding Graph Edit Distance Based on Rings and Machine Learning

The graph edit distance (GED) is a flexible distance measure which is widely used for inexact graph matching. Since its exact computation is [Formula: see text]-hard, heuristics are used in practice. A popular approach is to obtain upper bounds for GED via transformations to the linear sum assignment problem with error-correction (LSAPE). Typically, local structures and distances between them are employed for carrying out this transformation, but recently also machine learning techniques have been used. In this paper, we formally define a unifying framework LSAPE-GED for transformations from GED to LSAPE. We also introduce rings, a new kind of local structures designed for graphs where most information resides in the topology rather than in the node labels. Furthermore, we propose two new ring-based heuristics RING and RING-ML, which instantiate LSAPE-GED using the traditional and the machine learning-based approach for transforming GED to LSAPE, respectively. Extensive experiments show that using rings for upper bounding GED significantly improves the state of the art on datasets where most information resides in the graphs’ topologies. This closes the gap between fast but rather inaccurate LSAPE-based heuristics and more accurate but significantly slower GED algorithms based on local search.

Deep Learning Based Resources Allocation for Internet-of-Things Deployment Underlaying Cellular Networks

Resources allocation (RA) is a challenging task in many fields and applications including communications and computer networks. The conventional solutions of such problems usually come with a time and memory cost, especially for massive networks such as Internet-of-Things (IoT) networks. In this paper, two RA deep network models are proposed for enabling a clustered underlay IoT deployment, where a group of IoT nodes are uploading information to a centralized gateway in their vicinity by reusing the communication channels of conventional cellular users. The RA problem is formulated as a two-dimensional matching problem, which can be expressed as a traditional linear sum assignment problem (LSAP). The two proposed models are based on the recurrent neural network (RNN). Specifically, we investigate the performance of two long short-term memory (LSTM) based architectures. The results show that the proposed techniques could be used as replacement of the well-known Hungarian algorithm for solving LSAPs due to its ability to find the solution for the problems with different sizes, high accuracy, and very fast execution time. Additionally, the results show that the obtained accuracy outperforms the state-of-the-art deep network techniques.

Deep Neural Network Approximated Dynamic Programming for Combinatorial Optimization

In this paper, we propose a general framework for combining deep neural networks (DNNs) with dynamic programming to solve combinatorial optimization problems. For problems that can be broken into smaller subproblems and solved by dynamic programming, we train a set of neural networks to replace value or policy functions at each decision step. Two variants of the neural network approximated dynamic programming (NDP) methods are proposed; in the value-based NDP method, the networks learn to estimate the value of each choice at the corresponding step, while in the policy-based NDP method the DNNs only estimate the best decision at each step. The training procedure of the NDP starts from the smallest problem size and a new DNN for the next size is trained to cooperate with previous DNNs. After all the DNNs are trained, the networks are fine-tuned together to further improve overall performance. We test NDP on the linear sum assignment problem, the traveling salesman problem and the talent scheduling problem. Experimental results show that NDP can achieve considerable computation time reduction on hard problems with reasonable performance loss. In general, NDP can be applied to reducible combinatorial optimization problems for the purpose of computation time reduction.

Generative neural network based spectrum sharing using linear sum assignment problems

Spectrum management and resource allocation (RA) problems are challenging and critical in a vast number of research areas such as wireless communications and computer networks. The traditional approaches for solving such problems usually consume time and memory, especially for large-size problems. Recently different machine learning approaches have been considered as potential promising techniques for combinatorial optimization problems, especially the generative model of the deep neural networks. In this work, we propose a resource allocation deep autoencoder network, as one of the promising generative models, for enabling spectrum sharing in underlay device-to-device (D2D) communication by solving linear sum assignment problems (LSAPs). Specifically, we investigate the performance of three different architectures for the conditional variational autoencoders (CVAE). The three proposed architecture are the convolutional neural network (CVAE-CNN) autoencoder, the feed-forward neural network (CVAE-FNN) autoencoder, and the hybrid (H-CVAE) autoencoder. The simulation results show that the proposed approach could be used as a replacement of the conventional RA techniques, such as the Hungarian algorithm, due to its ability to find solutions of LASPs of different sizes with high accuracy and very fast execution time. Moreover, the simulation results reveal that the accuracy of the proposed hybrid autoencoder architecture outperforms the other proposed architectures and the state-of-the-art DNN techniques.

Bidirectional Long Short-Term Memory Neural Networks for Linear Sum Assignment Problems

Many resource allocation problems can be modeled as a linear sum assignment problem (LSAP) in wireless communications. Deep learning techniques such as the fully-connected neural network and convolutional neural network have been used to solve the LSAP. We herein propose a new deep learning model based on the bidirectional long short-term memory (BDLSTM) structure for the LSAP. In the proposed method, the LSAP is divided into sequential sub-assignment problems, and BDLSTM extracts the features from sequential data. Simulation results indicate that the proposed BDLSTM is more memory efficient and achieves a higher accuracy than conventional techniques.

Comparing heuristics for graph edit distance computation

Because of its flexibility, intuitiveness, and expressivity, the graph edit distance (GED) is one of the most widely used distance measures for labeled graphs. Since exactly computing GED is NP-hard, over the past years, various heuristics have been proposed. They use techniques such as transformations to the linear sum assignment problem with error correction, local search, and linear programming to approximate GED via upper or lower bounds. In this paper, we provide a systematic overview of the most important heuristics. Moreover, we empirically evaluate all compared heuristics within an integrated implementation.

A graph space optimal transport distance as a generalization of Lp distances: application to a seismic imaging inverse problem

Optimal transport distance is an appealing tool to measure the discrepancy between datasets in the frame of inverse problems, for its ability to perform global comparisons and its convexity with respect to shifted patterns in the compared quantities. However, solving inverse problems might require to compare signed quantities, while the optimal transport theory has been developed for the comparison of probability measures. In this study we propose to circumvent this difficulty by applying optimal transport to the comparison of the graph of the data rather than the data itself. We investigate this approach in the frame of seismic imaging, where each channel of the oscillatory data is interpreted as a discrete point cloud. We demonstrate that the corresponding misfit function can be computed through the solution of series of linear sum assignment problem (LSAP), while, based on the adjoint state technique, its gradient can be computed from the assignment solution of these LSAP. We illustrate how this approach yields a convex misfit function in the frame of seismic imaging using the full waveform. We show how an efficient strategy, based on a specific LSAP solver, the auction algorithm, can be designed. We illustrate the interest of the approach on a realistic 2D visco-acoustic seismic imaging problem. The proposed strategy relaxes the constraint on the accuracy of the initial model, outperforming the conventional least-squares approach and a previously proposed optimal transport based approach. The computational time increases by only a few percents compared with the least-squares approach, opening the way to applications to 3D field data in the near future.

A new modified optimal perfect matching in partial feasible matching for solving fuzzy linear sum assignment problems

A new modified optimal perfect matching in partial feasible matching for solving fuzzy linear sum assignment problems

Deep Neural Networks for Linear Sum Assignment Problems

Many resource allocation issues in wireless communications can be modeled as assignment problems and can be solved online with global information. However, traditional methods for assignment problems take a lot of time to find the optimal solutions. In this letter, we solve the assignment problem using machine learning approach. Specifically, the linear sum assignment problems (LSAPs) are solved by the deep neural networks (DNNs). Since LSAP is a combinatorial optimization problem, it is first decomposed into several sub-assignment problems. Each of them is a classification problem and can be solved effectively with DNNs. Two kinds of DNNs, feed-forward neural network and convolutional neural network, are implemented to deal with the sub-assignment problems, respectively. Based on computer simulation, DNNs can effectively solve LSAPs with great time efficiency and only slight loss of accuracy.

Fast linear sum assignment with error-correction and no cost constraints

We propose an algorithm that efficiently solves the linear sum assignment problem with error-correction and no cost constraints. This problem is encountered for instance in the approximation of the graph edit distance. The fastest currently available solvers for the linear sum assignment problem require the pairwise costs to respect the triangle inequality. Our algorithm is as fast as these algorithms, but manages to drop the cost constraint. The main technical ingredient of our algorithm is a cost-dependent factorization of the node substitutions.

Coverage of Targets in Mobile Sensor Networks With Restricted Mobility

In this paper, we consider the problem of covering all regions of interests (targets) by relocating a set of mobile sensors such that total movement made by them is minimized. This problem itself is a challenging one and addressed recently by some researchers under free mobility model. We consider a more restricted version of the problem where sensors can move only in two mutually perpendicular directions. We first show that the optimal point to which a sensor must move to cover a specific target is different under this model from the one where sensors can move freely, and characterize such a point. On the basis of this observation, we have developed heuristics to solve the problem. The heuristics run in two phases; the first phase ensures coverage and the second phase, connectivity. In both the phases, the sensors can move only with restricted mobility. We have run a set of experiments to evaluate the performance of the proposed algorithm and found that the total movement made in the first phase is comparable to the solution given by an IPP ( Integer Programming Problem ). For the second phase, we have presented two heuristics MinCon and MinCon_m. The algorithm MinCon works by finding connected components of the graph consisting of sensor nodes. It then identifies destination locations where some sensors must be placed so that all necessary components become connected. Once the destinations are known, the problem is solved by mapping it to an LSAP (Linear Sum Assignment Problem). The other heuristic MinCon_m improves over MinCon by moving only a subset of sensors to their destinations using the solution of LSAP. It then finds the movement of the remaining sensors applying a technique used in the first phase.

Critical objective function values in linear sum assignment problems

The linear sum assignment problem has been well studied in combinatorial optimization. Because of the integrality property, it is a linear programming problem with a variety of efficient algorithms to solve it. In the given research, we present a reformulation of the linear sum assignment problem and a Lagrangian relaxation algorithm for its reformulation. An important characteristic of the new Lagrangian relaxation method is that the optimal Lagrangian multiplier yields a critical bottleneck value. Lagrangian relaxation has only one Lagrangian multiplier, which can only take on a limited number of values, making the search for the optimal multiplier easy. The interpretation of the optimal Lagrangian parameter is that its value is equal to the price that must be paid for all objects in the problem to be assigned.

On the Impact of Using Utilities Rather than Costs for Graph Matching

The concept of graph edit distance constitutes one of the most flexible graph matching paradigms available. The major drawback of graph edit distance, viz. the exponential time complexity, has been recently overcome by means of a reformulation of the edit distance problem to a linear sum assignment problem. However, the substantial speed up of the matching is also accompanied by an approximation error on the distances. Major contribution of this paper is the introduction of a transformation process in order to convert the underlying cost model into a utility model. The benefit of this transformation is that it enables the integration of additional information in the assignment process. We empirically confirm the positive effects of this transformation on five benchmark graph sets with respect to the accuracy and run time of a distance based classifier.