Network Flow Research Articles

HAtt-Flow: Hierarchical Attention-Flow Mechanism for Group-Activity Scene Graph Generation in Videos.

Group-activity scene graph (GASG) generation is a challenging task in computer vision, aiming to anticipate and describe relationships between subjects and objects in video sequences. Traditional video scene graph generation (VidSGG) methods focus on retrospective analysis, limiting their predictive capabilities. To enrich the scene-understanding capabilities, we introduced a GASG dataset extending the JRDB dataset with nuanced annotations involving appearance, interaction, position, relationship, and situation attributes. This work also introduces an innovative approach, a Hierarchical Attention-Flow (HAtt-Flow) mechanism, rooted in flow network theory to enhance GASG performance. Flow-attention incorporates flow conservation principles, fostering competition for sources and allocation for sinks, effectively preventing the generation of trivial attention. Our proposed approach offers a unique perspective on attention mechanisms, where conventional "values" and "keys" are transformed into sources and sinks, respectively, creating a novel framework for attention-based models. Through extensive experiments, we demonstrate the effectiveness of our Hatt-Flow model and the superiority of our proposed flow-attention mechanism. This work represents a significant advancement in predictive video scene understanding, providing valuable insights and techniques for applications that require real-time relationship prediction in video data.

A path-based simulation approach for multistate flow network reliability estimation without using boundary points

A multistate flow network is useful for the effective and efficient model construction and reliability evaluation of large and complex systems. To evaluate the reliability of a multistate flow network, boundary points for specified demands are generated in the existing path- and cut-based methodologies. Using the boundary points, the system reliability can be calculated using analytical or simulation methodologies. However, evaluating reliability using boundary points is an NP-hard problem. To improve the time efficiency of reliability estimation, a path-based simulation approach without boundary points is proposed in this study, where the minimal path without any cycles is used. The contributions of this study are threefold: First, the proposed path-based simulation complements the cut-based simulation to improve the applicability of reliability estimation for various network topologies. Second, the proposed simulation algorithm presents linear time complexity, whereas conventional boundary-based analytical methodologies or simulations consume exponential/factorial time. Third, the time attribute is included in the proposed simulation approach to analyze the behavior of reliability degradation over time. The experimental results, including those of a case study, indicate that the proposed path-based simulation is more effective and efficient than existing boundary-based approaches, particularly for large and complex systems.

STBGRN: A Traffic Prediction Model Based on Spatiotemporal Bidirectional Gated Recurrent Units and Graph Convolutional Residual Networks

With the development of society and the advancement of urbanization, the development of intelligent transportation system has attracted much attention. Efficient and accurate traffic flow prediction is one of the core tasks in the research of intelligent transportation system. Most of the existing spatiotemporal traffic flow prediction models do not make full use of various periodic spatiotemporal dynamic characteristics of traffic flow, and it is difficult to effectively capture the complex spatiotemporal changes of traffic flow. To accurately predict the traffic flow of complex urban network, this paper proposes a traffic prediction model (STBGRN) based on spatiotemporal bidirectional gated cycle unit (ST-BiGRU) and graph convolution residual network (GCN-ResNet). The spatiotemporal information in traffic data is learned using the spatiotemporal bidirectional GRU coupled with the forward and backward information of the current time step, and the topology structure of the traffic network is captured by the graph convolution residual network, which is combined to complete the prediction task of the urban traffic network. In this paper, STBGRN was tested on two real data sets, SZ-taxi and Los-loop, and compared with other baseline methods, the RMSE index reached 3.857 and 5.461, and the MAE index reached 2.702 and 3.781, respectively. Accuracy index is 72.66% and 91.35%, R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}^{2}$$\\end{document} index is 0.858 and 0.845, var index is 0.858 and 0.849. The experimental results show that STBGRN model can obtain spatiotemporal dependence from complex traffic data, and can be used in spatiotemporal traffic data processing.

Kafka‐Shield: Kafka Streams‐based distributed detection scheme for IoT traffic‐based DDoS attacks

AbstractWith the rapid proliferation of insecure Internet of Things (IoT) devices, the security of Internet‐based applications and networks has become a prominent concern. One of the most significant security threats encountered in IoT environments is a Distributed Denial of Service (DDoS) attack. This attack can severely disrupt critical services and prevent smart devices from functioning normally, leading to severe consequences for businesses and individuals. It aims to overwhelm victims' resources, websites, and other services by flooding them with massive attack packets, making them inaccessible to legitimate users. Researchers have developed multiple detection schemes to detect DDoS attacks. As technology advances and other facilitating factors have increased, it is a challenge to identify such powerful attacks in real‐time. In this paper, we propose a novel distributed detection scheme for IoT network traffic‐based DDoS attacks by deploying it in a Kafka Streams processing framework named Kafka‐Shield. The Kafka‐Shield comprises two stages: design and deployment. Firstly, the detection scheme is designed on the Hadoop cluster employing a highly scalable H2O.ai machine learning platform. Secondly, a portable, scalable, and distributed detection scheme is deployed on the Kafka Streams processing framework. To analyze the incoming traffic data and categorize it into nine target classes in real time. Additionally, Kafka‐Shield stores each network flow with significant input features and the predicted outcome in the Hadoop Distributed File System (HDFS). It enables the development of new models or updating current ones. To validate the effectiveness of the Kafka‐Shield, we performed critical analysis using various configured attack scenarios. The experimental results affirm Kafka‐Shield's remarkable efficiency in detecting DDoS attacks. It has a detection rate of over 99% and can process 0.928 million traces in nearly 3.027 s.

Scalability and Performance Optimization Strategies in Large-Scale System Architectures

This paper aims to break away from traditional thinking paradigms by introducing theories and methods from complexity science to provide innovative and effective solutions for scalability and performance optimization of large-scale system architectures. The paper first constructs a complex network model for large-scale system architecture, which includes nodes (services), edges (interactions), and global attributes, along with dynamic models reflecting key metrics such as system performance and scalability, providing a theoretical foundation for subsequent research. Subsequently, from a complexity perspective, it innovatively proposes scalability strategies, including adaptive scalability strategies for complex network optimization, data-driven complex system regulation, and elastic computing and service orchestration mechanisms. In terms of performance optimization, it applies tools such as complex systems observation theory and network flow theory to explore insights and breakthroughs in complexity related to full-link performance monitoring and diagnostics, asynchronous communication, task scheduling, and software-hardware collaborative optimization. Finally, the paper summarizes the research findings, distilling the core concepts and methodological innovations of scalability and performance optimization strategies from a complexity perspective. It also looks ahead to the prospects of further integrating complexity science and information technology in the future, along with potential research topics in new scenarios and challenges.

Risk identification of public opinion on social media: a new approach based on cross-spatial network analysis

PurposeThis study aims to use geographical information on social media for public opinion risk identification during a crisis.Design/methodology/approachThis study constructs a double-layer network that associates the online public opinion with geographical information. In the double-layer network, Gaussian process regression is used to train the prediction model for geographical locations. Second, cross-space information flow is described using local government data availability and regional internet development indicators. Finally, the structural characteristics and information flow of the double-layer network are explored to capture public opinion risks in a fine-grained manner. This study used the early stages of the COVID-19 outbreak for validation analyses, and it collected more than 90,000 pieces of public opinion data from microblogs.FindingsIn the early stages of the COVID-19 outbreak, the double-layer network exhibited a radiating state, and the information dissemination was more dependent on the nodes with higher in-degree. Moreover, the double-layer network structure showed geographical differences. The risk contagion was more significant in areas where information flow was prominent, but the influence of nodes was reduced.Originality/valuePublic opinion risk identification that incorporates geographical scenarios contributes to enhanced situational awareness. This study not only effectively extends geographical information on social media, but also provides valuable insights for accurately responding to public opinion.

Multi-class vulnerability prediction using value flow and graph neural networks

In recent years, machine learning models have been increasingly used to detect security vulnerabilities in software, due to their ability to achieve high performance and lower false positive rates compared to traditional program analysis tools. However, these models often lack the capability to provide a clear explanation for why a program has been flagged as vulnerable, leaving developers with little reasoning to work with. We present a new method which not only identifies the presence of vulnerabilities in a program, but also the specific type of error, considering the whole program rather than just individual functions. Our approach utilizes graph neural networks that employ inter-procedural value flow graphs, and instruction embedding from the LLVM Intermediate Representation, to predict a class. By mapping these classes to the Common Weakness Enumeration list, we provide a clear indication of the security issue found, saving developers valuable time which would otherwise be spent analyzing a binary vulnerable/non-vulnerable label. To evaluate our method’s effectiveness, we used two datasets: one containing memory-related errors (out of bound array accesses), and the other a range of vulnerabilities from the Juliet Test Suite, including buffer and integer overflows, format strings, and invalid frees. Our model, implemented using PyTorch and the Gated Graph Sequence Neural Network from Torch-Geometric, achieved a precision of 96.35 and 91.59% on the two datasets, respectively. Compared to common static analysis tools, our method produced roughly half the number of false positives, while identifying approximately three times the number of vulnerable samples. Compared to recent machine learning systems, we achieve similar performance while offering the added benefit of differentiating between classes. Overall, our approach represents a meaningful improvement in software vulnerability detection, providing developers with valuable insights to better secure their code.

Mapping analytical methods between input–output economics and network science

AbstractThe input–output (IO) model can be used to examine the flow of products and services within an economy, resembling a network with industries as nodes and transactions as links. Diverging significantly from commonly studied networks such as social, protein, and power grids, IO networks exhibit intricate interconnectivity, involving weighted nodes and both directional and weighted links. This uniqueness necessitates careful consideration when applying complex network analysis techniques to IO systems. We critically review current complex network metrics and attempt to link them with existing IO approaches. Based on our assessment, certain network metrics, such as degree centrality and eigenvector centrality, have been explicitly integrated into the IO theory. In contrast, there exist metrics whose definitions and interpretations expand when applied in the context of IO analysis, including closeness and betweenness centrality. Additionally, network metrics are usually used to study topological features, identify key sectors, and construct novel metrics to study related issues. Network metrics used in IO analysis can identify important driver and transmission sectors in resource flow and environmental emission network, facilitating the development of targeted and reliable strategies. Besides, network metrics are used to quantify topological features and structural changes of the IO network which help strengthen the supply chain and mitigate both direct and indirect impacts of disruptions. Our ultimate goal is to establish connections and offer a roadmap for developing network‐based tools in IO analysis.

An Iterative Adaptive Dynamic Programming Approach for Macroscopic Fundamental Diagram-Based Perimeter Control and Route Guidance

Macroscopic fundamental diagrams (MFDs) have been widely adopted to model the traffic flow of large-scale urban networks. Coupling perimeter control and regional route guidance (PCRG) is a promising strategy to decrease congestion heterogeneity and reduce delays in large-scale MFD-based urban networks. For MFD-based PCRG, one needs to distinguish between the dynamics of (a) the plant that represents reality and is used as the simulation tool and (b) the model that contains easier-to-measure states than the plant and is used for devising controllers, that is, the model-plant mismatch should be considered. Traditional model-based methods (e.g., model predictive control (MPC)) require an accurate representation of the plant dynamics as the prediction model. However, because of the inherent network uncertainties, such as uncertain dynamics of heterogeneity and demand disturbance, MFD parameters could be time-varying and uncertain. Conversely, existing data-driven methods (e.g., reinforcement learning) do not consider the model-plant mismatch and the limited access to plant-generated data, for example, subregional OD-specific accumulations. Therefore, we develop an iterative adaptive dynamic programming (IADP)-based method to address the limited data source induced by the model-plant mismatch. An actor-critic neural network structure is developed to circumvent the requirement of complete information on plant dynamics. Performance comparisons with other PCRG schemes under various scenarios are carried out. The numerical results indicate that the IADP controller trained with a limited data source can achieve comparable performance with the “benchmark” MPC approach using perfect measurements from the plant. The results also validate the IADP’s robustness against various uncertainties (e.g., demand noise, MFD error, and trip distance heterogeneity) when minimizing the total time spent in the urban network. These results demonstrate the great potential of the proposed scheme in improving the efficiency of multiregion MFD systems. Funding: The work was jointly funded by the National Natural Science Foundation of China under [Grant 72071214] (R. Zhong), the Dit4Tram project from the European Union’s Horizon 2020 Research and Innovation Programme under [Grant 953783] (N. Geroliminis), and the Research Student Attachment Programme of The Hong Kong Polytechnic University (C. Chen). Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0091 .

Cost-efficient flow migration for SFC dynamical scheduling in geo-distributed clouds

Combining Network Function Virtualization (NFV) and Software Defined Network (SDN) enables the delivery of network services in a flexible and cost-efficient manner. NFV allows elasticity scheduling of Virtual Network Function (VNF) instances to adopt the dynamic variation of network flows, such as VNF instance scale out or in and load balancing. To implement the elasticity scheduling, existing flows need to be re-routed through the VNF instances. One major problem is how to select appropriate flows for migration to reduce migration cost and improve network performance after migration. In this paper, we propose a Cost-efficient Flow Migration framework, CFM, to jointly optimize flow migration cost and network performance after migration (including flow routing cost and maximum VNF instance load) for flow migration in Service Function Chain manner. Experimental results demonstrate that CFM can reduce flow routing cost after migration by 43%∼62% compared with previous works, while achieving similar flow migration cost in scale out/in scenario. In load balancing scenario, CFM can also reduce flow migration cost by 65%∼79% and flow routing cost after migration by 43%∼79% compared with previous works, while ensuring that the maximum VNF instance load does not significantly increase.

The Maximum Attainable Flow and Minimal Cost Problem in a Network

This paper, presents an efficient algorithm that solves such a large class of optimization problems. Ford-Fulkerson determines the maximum flow in a network by iteratively augmenting flow paths until no further improvement is possible. On the other hand, Dijkstra's algorithm excels in finding the shortest path in a weighted graph, making it suitable for minimizing costs in network traversal. However, this paper simultaneously optimizes both objectives (flow and cost) dependently in unique iterations by considering all constraints and objectives holistically. The aim of this work is to develop efficient algorithms that can handle complex optimization problems in transportation, network design, and other fields, ultimately improving resource utilization and minimizing costs as its crucial for enhancing decision-making processes, improving efficiency in resource utilization, and achieving cost savings in diverse applications ranging from transportation networks to production planning. This paper deals about formulating the linear programming for the optimizations problems and finding the maximum amount of flow that can be sent from a source node to a sink node while minimizing the total cost of sending that flow by using simplex method (Two phase method). Through computational experiments and case studies, everybody demonstrate the effectiveness and efficiency of the proposed approach in solving real-world network flow problems. Our method yields efficient algorithms with in smallest numbers of iterations and time that enable the optimal allocation of resources within networks, achieving both maximum flow and minimum cost simultaneously.

Analysis of geothermal heat recovery from abandoned coal mine water for clean heating and cooling: A case from Shandong, China

Exploiting heat from abandoned mine water using heat pumps is attracting increasing attention worldwide. China has a large number of abandoned coal mines, but there are few applications of geothermal heat recovery from mine water. Here, we report a new case from Shandong, North China. Based on actual geological and underground space structures, numerical analysis is performed to study the flow and heat transfer in the complex connection network among roadways. For given temperature differences on the source side, the underground heat transfer is greatly influenced by flow rates in roadways. Under the acceptable performances and long-term stability of heat pumps, the maximum heat transfer capacity of roadways reaches 697.3 kW at the flow rate of 100 m3/h, with the power per unit length of 151.3 W/m, indicating a promising heat recovery potential. When switching between the extraction and injection well, both fluid directions and the distribution of flow rates in roadways change obviously, thereby affecting the underground heat transfer. Besides dominant flow paths, there exist weak flow paths, which can be identified by numerical analysis, and necessary blocking can be applied to optimize the flow and heat transfer. Excessively long horizontal straight roadways for heat exchange should be avoided.

Drone resupply with multiple trucks and drones for on-time delivery along given truck routes

Drones have been increasingly used for deliveries; however, delivering packages directly to customers is still challenging, particularly in densely populated urban areas. To overcome this, drone resupply has been proposed, where drones carry packages to trucks en route, and then trucks make the final deliveries. Existing studies have only considered the case of one truck and one drone. In this study, we investigate drone resupply with multiple trucks and drones for the on-time delivery of late-available packages. Considering practical operations in urban areas, we focus on a situation where trucks deliver packages along given routes. This raises the drone resupply scheduling problem, which aims to maximise the total value of the late-available packages that can be delivered on time. We formally define the problem and analyse its optimality properties. Then, we develop an exact solution approach based on a time-expanded network flow model and design a greedy heuristic algorithm. We validate the efficiency and effectiveness of the proposed solutions through computational studies. Operational insights and guidance are derived for the application of drones in on-time delivery.

Efficient river hydrodynamics modelling in realistic river systems using a Fourier neural operator-based network

Effective river management relies heavily on the accurate simulation of river flow dynamics to develop scenario-based strategies and inform decision making. Deep learning (DL) models, as alternatives to conventional simulation techniques, offer a compelling blend of precision and efficiency. This study introduces FNOCL (Fourier Neural Operator with ConvLSTM units), a novel DL neural network for modelling unsteady natural river flows. The network is adept at handling the complexities of spatial and temporal variations. FNOCL builds upon the Fourier neural operator (FNO) by incorporating convolutional long short-term memory (ConvLSTM) layers, combining robust performance with high proficiency in terms of capturing spatiotemporal patterns. Notably, FNOCL accommodates complex river cross-section profiles, thus enabling the accurate modelling of flow dynamics within intricate river morphologies. Our study applies FNOCL to two distinct river networks with varying morphology complexity levels. With reference to the HEC-RAS model, FNOCL showcases its ability to attain high accuracy in model prediction tasks and superior generalization with regard to addressing the uncertainty associated with inflow variations and cross-sectional changes. In comparative analyses with benchmark models (i.e., FNO and ConvLSTM), FNOCL performs most efficiently during the training process and obtains the most accurate water level and river flow predictions in the spatiotemporal domain. Furthermore, FNOCL exhibits a substantial speedup over HEC-RAS, notably reaching up to 50 times in a complex river network. These results highlight FNOCL as an efficient surrogate for conventional simulators, facilitating precise analyses across various scenarios. It provides efficient computations for system responses within complex river flow networks, thereby enhancing applications in river management, such as flood risk assessment, flood control, and the planning and design of hydraulic control structures.

A framework for detecting zero-day exploits in network flows

Zero-day attack detection solutions aim to proactively identify unknown threats targeting valuable assets within a given system. While many Intrusion Detection System (IDS) solutions leverage learning techniques to build novel attack detection systems, they often focus on enhancing accuracy for specific attack types, overlooking the potential for multiple attack scenarios. Therefore, we introduce a novel framework for detecting zero-day attacks that evade current detection systems. Our framework enhances attack identification and qualification through a hybrid learning approach, where supervised learning ensures detection of known attacks and unsupervised learning. It encompasses intrusion detection phases from data collection to new attack class detection by identifying anomalies in real-time network flow data. Unsupervised learning, which involves grouping similar data points into clusters, establishes minimum distances within these clusters. This process triggers cluster division when certain thresholds are reached. Finally, an online supervised learning process validates our approach’s effectiveness in identifying anomalies associated with zero-day attack flows.This approach significantly reduces the False Detection Rate (FDR) without solely focusing on optimizing machine learning (ML) and deep learning (DL) algorithms hyper-parameters. We evaluated our framework on two datasets: one from a real industrial context at IBM and the NSL-KDD dataset. The results demonstrate our framework’s ability to detect anomalies in previously zero-day attack targets. On average, we identified 71 anomalous flows per target, achieving an overall average online learning accuracy of 98.4% for the IBM dataset and 96.6% for the NSL-KDD dataset, thereby validating the detection of these new attack scenarios.

Evaluating the Performance and Challenges of Machine Learning Models in Network Anomaly Detection

The application of machine learning algorithms for anomaly detection in network traffic data is examined in this study. Using a collection of network flow records that includes attributes such as IP addresses, ports, protocols, and timestamps, the study makes use of correlation heatmaps, box plots, and data visualization to identify trends in numerical characteristics. After preprocessing, which includes timestamp conversion to Unix format, three machine learning models Support Vector Machine (SVM), Gaussian Naive Bayes, and Random Forest are used for anomaly identification. The Random Forest Classifier outperforms SVM and Naive Bayes classifiers with better precision and recall for anomaly diagnosis, achieving an accuracy of 87%. Confusion matrices and classification reports are used to evaluate the models, and they show that the Random Forest Classifier performs better than the other models in identifying abnormalities in network traffic. These results provide significant value to the field of cybersecurity by highlighting the effectiveness of machine learning models specifically, the Random Forest Classifier in boosting anomaly detection capacities for network environment security.

Liner shipping network vulnerability to component disruptions: A China-Europe container flow analysis

This study conducts a vulnerability analysis of the China-Europe liner shipping network, including all relevant liner shipping services and China Railway Express services. The standard multicommodity network flow model is extended to assess network vulnerability and the relative importance of ports and services by simulating container flow redistribution in various disruption scenarios. The results show the network is highly resilient to both individual port disruptions and individual service disruptions. Additionally, the distinct shipping network structures of the three shipping alliances result in varying degrees of vulnerability, highlighting the significance of diversified market suppliers in enhancing the overall network resilience. Specifically, the Ocean Alliance is vital in facilitating China-Europe trade, especially along the Mediterranean route, and is more resilient to individual port disruptions.

Distributionally robust disaster relief planning under the Wasserstein set

We study a two-stage natural disaster management problem modeled as a stochastic program, where the first stage consists of a facility location problem, deciding where to open facilities and pre-allocate resources such as medical and food kits, and the second stage is a fixed-charge transportation problem, routing resources to affected areas after observing a disaster. Our model has binary variables present in both stages. Due to the lack of data, classical stochastic programming approaches may be ill-suited, and we propose a two-stage distributionally robust formulation with a Wasserstein ambiguity set, where we consider distributions consistent with historical data and a tunable parameter to control the level of risk aversion. We develop a tailored column-and-constraint generation (CCG) algorithm to solve an extensive reformulation, where scenarios are iteratively generated. We handle the presence of binary variables in the second stage by leveraging the structure of our support set and second-stage problem, and provide conditions under which the optimal value of the latter is concave with respect to the intensity of the disaster, leading to an efficient scenario generation procedure. We also show that our results extend to the case where the second stage is a fixed-charge network flow problem. We perform extensive computational experiments demonstrating the computational advantage of our method over classical CCG implementations on synthetic instances, and illustrate the benefits of our approach on a popular case study from the literature of hurricane threats on the Gulf of Mexico in the United States.

Applying self-supervised learning to network intrusion detection for network flows with graph neural network

Graph Neural Networks (GNNs) have garnered intensive attention for Network Intrusion Detection System (NIDS) due to their suitability for representing the network traffic flows. However, most present GNN-based methods for NIDS are supervised or semi-supervised. Network flows need to be manually annotated as supervisory labels, a process that is time-consuming or even impossible, making NIDS difficult to adapt to potentially complex attacks, especially in large-scale real-world scenarios. The existing GNN-based self-supervised methods focus on the binary classification of network flow as benign or not, and thus fail to reveal the types of attack in practice. This paper studies the application of GNNs to identify the specific types of network flows in an unsupervised manner. We first design an encoder to obtain graph embedding, that introduces the graph attention mechanism and considers the edge information as the only essential factor. Then, a self-supervised method based on graph contrastive learning is proposed. The method samples center nodes, and for each center node, generates subgraph by it and its direct neighbor nodes, and corresponding contrastive subgraph from the interpolated graph, and finally constructs positive and negative samples from subgraphs. Furthermore, a structured contrastive loss function based on edge features and graph local topology is introduced. To the best of our knowledge, it is the first GNN-based self-supervised method for the multiclass classification of network flows in NIDS. Detailed experiments conducted on four real-world datasets (NF-Bot-IoT, NF-Bot-IoT-v2, NF-CSE-CIC-IDS2018, and NF-CSE-CIC-IDS2018-v2) systematically compare our model with the state-of-the-art supervised and self-supervised models, illustrating the considerable potential of our method. Our code is accessible through https://github.com/renj-xu/NEGSC.

On Density-based Local Community Search

Local community search (LCS) finds a community in a given graph G local to a set R of seed nodes by optimizing an objective function. The objective function f(S) for an induced subgraph S encodes the set inclusion criteria of R to a classic community measurement of S such as the conductance and the density. An ideal algorithm for optimizing f(S) is strongly local, that is, the complexity is dependent on R as opposed to G. This paper formulates a general form of objective functions for LCS using configurations and then focuses on a set C of density-based configurations, each corresponding to a density-based LCS objective function. The paper has two main results. i) A constructive classification of C: a configuration in C has a strongly local algorithm for optimizing its corresponding objective function if and only if it is in C L ⊆ C. ii) A linear programming-based general solution for density-based LCS that is strongly local and practically efficient. This solution is different from the existing strongly local LCS algorithms, which are all based on flow networks.