Representative Node Research Articles

Analysis of the response of wind-induced vibrations on flexible photovoltaic mounts

Abstract This article investigates a flexible photovoltaic bracket’s response to wind vibration. A finite element model is established using SAP2000 software for time course analysis. Representative units and nodes were selected to analyze internal force response, displacement response, and acceleration response. The prestress and span change rule of the flexible photovoltaic bracket are also explored, and quantitative research is conducted on the size of prestress and span size. The magnitude of the prestress affects a structure’s responsiveness to wind vibration. As prestress grows, so do deflection and acceleration, and the rate at which axial force is increasing also increases. Conversely, when prestress increases, the rate of deflection reduction falls. Consequently, considering the prestress size, it is advised that 50-kN prestressing be used for the support and wind cables. As the span rises, so do the mid-span span and the axial force of the wind cables, while acceleration also increases. The rate of mid-span deflection increases gradually with the flexible PV mount span, but the rate of axial force increase decreases. It is recommended to limit the span to below 50 m.

Finding core labels for maximizing generalization of graph neural networks

Graph neural networks (GNNs) have become a popular approach for semi-supervised graph representation learning. GNNs research has generally focused on improving methodological details, whereas less attention has been paid to exploring the importance of labeling the data. However, for semi-supervised learning, the quality of training data is vital. In this paper, we first introduce and elaborate on the problem of training data selection for GNNs. More specifically, focusing on node classification, we aim to select representative nodes from a graph used to train GNNs to achieve the best performance. To solve this problem, we are inspired by the popular lottery ticket hypothesis, typically used for sparse architectures, and we propose the following subset hypothesis for graph data: “There exists a core subset when selecting a fixed-size dataset from the dense training dataset, that can represent the properties of the dataset, and GNNs trained on this core subset can achieve a better graph representation”. Equipped with this subset hypothesis, we present an efficient algorithm to identify the core data in the graph for GNNs. Extensive experiments demonstrate that the selected data (as a training set) can obtain performance improvements across various datasets and GNNs architectures.

Optimal sensor placement for leak location in water distribution networks based on graph learning algorithm

Abstract The effective monitoring of urban water distribution networks (WDNs) relies heavily on pressure sensor placement. Nevertheless, a WDN may consist of hundreds of nodes, and it is not economically feasible to install sensors at each node. Therefore, how to identify an optimal location for sensor placement becomes a crucial issue. We use graph signal processing to analyze the pressure signals and introduce a framework for optimal sensor placement specifically designed for pressure signals. To address the limitation that pressure signals cannot be sampled directly, we propose a method to convert the signal into a band-limited signal that meets the requirements. Central to the method is learning a graph Fourier operator, and the effectiveness of the proposed method is proved theoretically. The graph Fourier operator enables the pressure data to become a smooth graph signal with variations in its topology. In addition, we design a graph filter based on the energy of the signal and obtain a band-limited signal that meets the requirements. To ensure the selection of representative nodes, we use a noise-robust graph sampling method to obtain the sensor node. Our method is further evaluated using the pressure data from Anytown versus Net3, showing strong performance in leak identification and signal reconstruction capabilities.

Dynamic Cluster Head Selection in WSN

A Wireless Sensor Network (WSN) comprises an ad-hoc network of nodes laden with sensors that are used to monitor a region mostly in the outdoors and often not easily accessible. Despite exceptions, several deployments of WSN continue to grapple with the limitation of finite energy derived through batteries. Thus, it is imperative that the energy of a WSN be conserved and its life prolonged. An important direction of work to this end is towards the transmission of data between nodes in a manner that minimum energy is expended. One approach to doing this is cluster-based routing, wherein nodes in a WSN are organised into clusters, and transmission of data from the node is through a representative node called a cluster-head. Forming optimal clusters and choosing an optimal cluster-head is an NP-Hard problem. Significant work is done towards devising mechanisms to form clusters and choosing cluster heads to reduce the transmission overhead to a minimum. In this article, an approach is proposed to create clusters and identify cluster heads that are near optimal. The approach involves two-stage clustering, with the clustering algorithm for each stage chosen through an exhaustive search. Furthermore, unlike existing approaches that choose a cluster-head on the basis of the residual energy of nodes, the proposed approach utilises three factors in addition to the residual energy, namely the distance of a node from the cluster centroid, the distance of a node from the final destination (base-station), and the connectivity of the node. The approach is shown to be effective and economical through extensive validation via simulations and through a real-world prototypical implementation.

Broad Learning System under Label Noise: A Novel Reweighting Framework with Logarithm Kernel and Mixture Autoencoder.

The Broad Learning System (BLS) has demonstrated strong performance across a variety of problems. However, BLS based on the Minimum Mean Square Error (MMSE) criterion is highly sensitive to label noise. To enhance the robustness of BLS in environments with label noise, a function called Logarithm Kernel (LK) is designed to reweight the samples for outputting weights during the training of BLS in order to construct a Logarithm Kernel-based BLS (L-BLS) in this paper. Additionally, for image databases with numerous features, a Mixture Autoencoder (MAE) is designed to construct more representative feature nodes of BLS in complex label noise environments. For the MAE, two corresponding versions of BLS, MAEBLS, and L-MAEBLS were also developed. The extensive experiments validate the robustness and effectiveness of the proposed L-BLS, and MAE can provide more representative feature nodes for the corresponding version of BLS.

Road Network Traffic Flow Prediction Method Based on Graph Attention Networks

With the acceleration of urbanization and the continuous growth of transportation demand, the traffic management of smart city road networks has become increasingly complex and critical. Traffic flow prediction, as an important component of smart transportation systems, is of great significance for optimizing traffic planning and improving traffic efficiency. The study collected and preprocessed traffic data in the smart city road network, including multi-dimensional information such as traffic flow, road conditions, and meteorological data. Then, based on the idea of graph neural networks, we constructed the topological structure of the urban road network and abstracted elements such as roads and intersections into nodes, using edges to represent their connection relationships, thus forming a graph dataset. Next, we introduced an attention mechanism to extract more representative node features through the weighted aggregation of node features, thereby achieving effective modeling of urban road network traffic flow. During the model training phase, we used real traffic datasets for experimental verification and integrated various information such as time, space, and road features into the model. The experimental results show that compared to traditional methods, this research prediction method has achieved better performance in traffic flow prediction tasks, with higher prediction accuracy and robustness. It has stronger applicability and effectiveness in different traffic scenarios. By integrating multi-dimensional information and introducing attention mechanisms, this method has significant advantages in improving the accuracy and robustness of traffic flow prediction, and has important practical significance and application prospects for the construction of smart transportation systems and the development of smart cities.

Towards Dynamic Spatial-Temporal Graph Learning: A Decoupled Perspective

With the progress of urban transportation systems, a significant amount of high-quality traffic data is continuously collected through streaming manners, which has propelled the prosperity of the field of spatial-temporal graph prediction. In this paper, rather than solely focusing on designing powerful models for static graphs, we shift our focus to spatial-temporal graph prediction in the dynamic scenario, which involves a continuously expanding and evolving underlying graph. To address inherent challenges, a decoupled learning framework (DLF) is proposed in this paper, which consists of a spatial-temporal graph learning network (DSTG) with a specialized decoupling training strategy. Incorporating inductive biases of time-series structures, DSTG can interpret time dependencies into latent trend and seasonal terms. To enable prompt adaptation to the evolving distribution of the dynamic graph, our decoupling training strategy is devised to iteratively update these two types of patterns. Specifically, for learning seasonal patterns, we conduct thorough training for the model using a long time series (e.g., three months of data). To enhance the learning ability of the model, we also introduce the masked auto-encoding mechanism. During this period, we frequently update trend patterns to expand new information from dynamic graphs. Considering both effectiveness and efficiency, we develop a subnet sampling strategy to select a few representative nodes for fine-tuning the weights of the model. These sampled nodes cover unseen patterns and previously learned patterns. Experiments on dynamic spatial-temporal graph datasets further demonstrate the competitive performance, superior efficiency, and strong scalability of the proposed framework.

PeerG: A P2P botnet detection method based on representation learning and graph contrastive learning

P2P botnets are distributed with complex topology and communication behavior, making them harder to detect and remove. Individuals or organizations can effectively detect P2P botnets by analyzing abnormal behaviors in network traffic. Existing works focus on extracting deterministic traffic interaction features, which are highly dependent on statistical features. Moreover, these methods are mainly aimed at generalized botnet detection and lack specificity for detecting P2P botnets. They ignore the topological information of P2P botnets, resulting in unsatisfactory detection accuracy. Among the few existing methods targeting P2P botnets, they consider the topological information but mainly rely on classical graph theory statistical features, such as degree, feature vector centrality, etc. This limits the generalization ability of the detection model. In this paper, we delve into the topological features of P2P botnets from the perspective of complex graph theory. We propose a P2P botnet detection method that combines representation learning and graph contrastive learning, dubbed PeerG. Specifically, we construct the communication graphs based on the flow interaction behavior between components of the P2P botnets. The Line algorithm is employed to embed the nodes of the communication graph into a low-dimensional representation vector space. Subsequently, the graph contrastive learning approach is utilized to optimize the feature extractor, enabling it to capture more representative node features. PeerG serves as a benchmark detection model for identifying P2P botnet nodes. Additionally, we devise two optimized contrastive detection strategies (PeerG-PreG and PeerG-PreF) based on graph-level and feature-level to boost the performance of PeerG. Extensive experiments demonstrate that PeerG brings significant improvements in detection accuracy over state-of-art detection methods. Furthermore, compared with PeerG, the detection strategies PeerG-PreG and PeerG-PreF have further improved detection performance, and achieve the best detection accuracy among multiple filtered P2P botnet types.

Rapid Geometric Evaluation of Transportation Infrastructure Based on a Proposed Low-Cost Portable Mobile Laser Scanning System.

Efficient geometric evaluation of roads and tunnels is crucial to traffic management, especially in post-disaster situations. This paper reports on a study of the geometric feature detection method based on multi-sensor mobile laser scanning (MLS) system data. A portable, low-cost system that can be mounted on vehicles and utilizes integrated laser scanning devices was developed. Coordinate systems and timestamps from numerous devices were merged to create 3D point clouds of objects being measured. Feature points reflecting the geometric information of measuring objects were retrieved based on changes in the point cloud's shape, which contributed to measuring the road width, vertical clearance, and tunnel cross section. Self-developed software was used to conduct the measuring procedure, and a real-time online visualized platform was designed to reconstruct 3D models of the measured objects, forming a 3D digital map carrying the obtained geometric information. Finally, a case study was carried out. The measurement results of several representative nodes are discussed here, verifying the robustness of the proposed system. In addition, the main sources of interference are also discussed.

Concordant dynamic changes of global network properties in the frontoparietal and limbic compartments: An EEG study

IntroductionDespite its complexity, deciphering nodal interaction is imperative to understanding a neural network. Network interaction is an even more complicated topic that must be addressed. This study aimed to examine the relationship between the brain waves of two canonical brain structures, i.e., the frontoparietal and limbic compartments, during a resting state. MethodsElectroencephalography (EEG) of 51 subjects in eye-closed condition was analyzed, and the eLORETA method was applied to convert the signals from the scalp to the brain. By way of community detection, representative neural nodes and the associated mean activities were retrieved. Total and lagged coherences were computed to indicate functional connectivity between those neural nodes. Two global network properties were elucidated based on the connectivity measures, i.e., global efficiency and mean functional connectivity strength. The temporal correlation of the global network indices between the two studied networks was explored. ResultsIt was found that there was a significant trend of positive correlation across the four metrics (lagged vs. total coherence x global efficiency vs. average connectivity). In other words, when the neural interaction in the FP network was stronger, so did that in the limbic network, and vice versa. Notably, the above interaction was not spectrally specific and only existed at a finer temporal scale (under hundreds of milliseconds level). ConclusionThe concordant change in network properties indicates an intricate balance between FP and LM compartments. Possible mechanisms and implications for the findings are discussed.

DHESN: A deep hierarchical echo state network approach for algal bloom prediction

A deep hierarchical echo state network (DHESN) is designed for rectifying the shortcomings of the shallow coupled structure with less reservoir dynamics. This design is with reference to algal bloom which is a complex ecological phenomenon. Accurate prediction of algal bloom can reduce the environmental impact and economic loss. Since the formation of algal bloom has chaotic characteristics, the ESN has been employed to realize its prediction function. First, the candidate variables with strong causal relationship have been screened by transfer entropy, and the redundant variables is eliminated. Then, a hierarchical reservoir structure is established that is inspired by the hierarchical characteristics from the brain. The hierarchical reservoir has realized the connection between the representative nodes of each subreservoir, and improved the information processing ability of the reservoir. Finally, the pruning and compression of the output weights have been realized by the elastic regularization method, which improves the robustness of the prediction model. The simulation results demonstrate that the DHESN has appreciable prediction accuracy in both the chaotic and the public algal bloom datasets. The DHESN contains richer dynamic characteristics, and can realize the self-organization of the network structure. It provides a novel idea to realize the prediction model of algal bloom with a high accuracy and low complexity.

3-D spatial correlation model for reducing the transmitting nodes in densely deployed WSN

In Wireless Sensor Networks, a large number of sensor nodes are distributed in the monitoring area to increase fault tolerance, coverage and communication range. In highly dense network, many nodes belong to common sensing region and record almost similar data of the event. Base station, however, can also identify the event features from data of a few representative nodes of the sensing region. The battery power of some sensor nodes may be saved by not sending multiple copies of the sensed information. In order to reduce transmitting nodes from the sensing region, an analytical model is presented to segregate the whole network into group of correlated regions. The minimum number of transmitting nodes are selected from probability based deployment of sensor nodes in 3D scenario and rest of the nodes are operated in sleep mode for saving the battery power. Effectiveness of proposed models is demonstrated with established technique of CHEF i.e. Cluster Head Election using Fuzzy Logic. Results show that number of nodes transmitting data from sense region can be reduced considerably with respect to threshold correlation value (ξ), which results in the energy saving of additional nodes and enhancement of network life. With implementation of proposed models, at ξ≤0.5, maximum transmitting nodes are 87% which saves battery power of at least 13% nodes.

Optimal sensor placement for leak location in water distribution networks based on EGAE clustering algorithm

In the water supply network system, the placement of pressure sensors is crucial to the optimization of the monitoring effect of the system running condition. Most of the existing studies select the placement of sensors according to the hydraulic state of the water distribution network, but do not fully consider and analyze the connectivity between nodes and the topology of the water distribution network. Aiming at the shortcomings of the existing pressure monitoring point layout methods, this paper proposes a pressure sensor layout method based on the Embedding Graph Autoencoder (EGAE) clustering method. Firstly, the EGAE deep clustering algorithm is used to cluster the network nodes based on the topology structure and hydraulic characteristics of the network. According to the clustering results, the network nodes are divided into different regions. Then, by calculating the correlation between nodes in the region, the representative nodes of each region are selected and set as sensor layout nodes. By comparing and analyzing the performance of experiments with other schemes, the results show that the EGAE deep clustering network can effectively integrate the topological structure characteristics and hydraulic characteristics of the water distribution network. The sensor nodes laid out in the scheme proposed in this paper can effectively carry out accurate leakage positioning in subsequent positioning models, and have higher leakage pipe segment identification accuracy and smaller precise positioning errors compared with other schemes.

Delegated Proof of Stake Consensus Mechanism Based on Community Discovery and Credit Incentive.

Consensus algorithms are the core technology of a blockchain and directly affect the implementation and application of blockchain systems. Delegated proof of stake (DPoS) significantly reduces the time required for transaction verification by selecting representative nodes to generate blocks, and it has become a mainstream consensus algorithm. However, existing DPoS algorithms have issues such as "one ballot, one vote", a low degree of decentralization, and nodes performing malicious actions. To address these problems, an improved DPoS algorithm based on community discovery is designed, called CD-DPoS. First, we introduce the PageRank algorithm to improve the voting mechanism, achieving "one ballot, multiple votes", and we obtain the reputation value of each node. Second, we propose a node voting enthusiasm measurement method based on the GN algorithm. Finally, we design a comprehensive election mechanism combining node reputation values and voting enthusiasm to select secure and reliable accounting nodes. A node credit incentive mechanism is also designed to effectively motivate normal nodes and drive out malicious nodes. The experimental simulation results show that our proposed algorithm has better decentralization, malicious node eviction capabilities and higher throughput than similar methods.

How do centrality measures help to predict similarity patterns in molecular chemical structural graphs?

The proposed work uses centrality measures based heuristic method to improve the efficiency of the solution for the similarity search problem in molecular chemical graphs by effectively identifying central candidate or representative candidate nodes, which simplify the complex processes involved while detecting a large-sized maximal common connected edge subgraph. After analyzing the structure of the two input molecular chemical graphs, a Tensor Product graph is created. This newly built graph is further analyzed to get the similarity pattern of the input graphs. It is an open problem to decide which centrality measure selects the best central candidate node in Tensor Product graphs to get a large maximal common connected edge graph. Since each centrality measure is analyses, the given graph is uniquely based on its own specific aspects. The proposed work offers directions on using various centrality measures to determine a big-sized maximal common connected subgraph for two molecular chemical input graphs. It also analyses seven centrality measures to select the best candidate node in the Tensor Product graph of two input chemical molecular graphs. Based on the obtained results, the betweenness centrality and degree centrality measures exclusively help to get large-sized similarity patterns.

GraphSR: A Data Augmentation Algorithm for Imbalanced Node Classification

Graph neural networks (GNNs) have achieved great success in node classification tasks. However, existing GNNs naturally bias towards the majority classes with more labelled data and ignore those minority classes with relatively few labelled ones. The traditional techniques often resort over-sampling methods, but they may cause overfitting problem. More recently, some works propose to synthesize additional nodes for minority classes from the labelled nodes, however, there is no any guarantee if those generated nodes really stand for the the corresponding minority classes. In fact, improperly synthesized nodes may result in insufficient generalization of the algorithm. To resolve the problem, in this paper we seek to automatically augment the minority classes from the massive unlabelled nodes of the graph. Specifically, we propose \textit{GraphSR}, a novel self-training strategy to augment the minority classes with significant diversity of unlabelled nodes, which is based on a Similarity-based selection module and a Reinforcement Learning(RL) selection module. The first module finds a subset of unlabelled nodes which are most similar to those labelled minority nodes, and the second one further determines the representative and reliable nodes from the subset via RL technique. Furthermore, the RL-based module can adaptively determine the sampling scale according to current training data. This strategy is general and can be easily combined with different GNNs models. Our experiments demonstrate the proposed approach outperforms the state-of-the-art baselines on various class-imbalanced datasets.

CD8 cell PET imaging with 89-Zr-crefmirlimab berdoxam (crefmirlimab) in patients with metastatic renal cell carcinoma (mRCC) receiving checkpoint inhibitors (CPIs): Association with response and tissue CD8 expression.

4551 Background: Novel imaging modalities using frequently expressed RCC antigens, such as CAIX, have shown promise in early-stage disease (Shuch B et al ASCO GU 2023). In advanced RCC, no tissue-based biomarkers have been well established to predict outcome with contemporary regimens, e.g., checkpoint inhibitors (CPIs) or targeted therapy (TT). We hypothesize that functional imaging of CD8 T-cells (CD8s) with crefmirlimab (a ~80 kDA 89Zr-labelled minibody with high affinity for CD8) may predict response given the essential role of CD8 T-cells (CD8s) in mediating CPI response. Methods: Eligible pts had pathologically verified RCC, metastatic disease and an intent to initiate standard of care CPI therapy. Patients received crefmirlimab PET/CT within 1 wk of CPI infusion and 4-6 weeks after initiating therapy. Baseline biopsy was mandated, along with repeat biopsy 0-2 weeks following the second PET/CT scan. PET signal was characterized as SUVmax, SUVpeak and SUVmean of the biopsied lesions, up to 5 index lesions and representative CD8 avid lymph nodes. Mean SUVmax in responders and non-responders were compared using students t-test (1-sided). CD8 expression in tissue was characterized as the number of positive cells per mm2; PET avidity and CD8 expression were compared using the Spearman correlation coefficient. Results: 17 pts (9 M: 8 F) were enrolled; most pts had clear cell histology (12; 71%) followed by unclassified (3; 17%) and papillary (2; 12%). The most commonly rendered CPI-based regimens were nivolumab alone (6 pts; 35%) and cabozantinib/nivolumab (3 pts; 17%). Follow-up data was available in 15 of the patients. By RECIST v1.1, 3 of 15 patients were classified as responders (best overall response [BOR] of complete response or partial response) and 12 patients were classified as non-responders (BOR of stable disease or progressive disease). Average SUVmax, SUVpeak and SUVmean per patient among all quantified index lesions and representative lymph nodes were 10.02, 6.95 and 6.11 for baseline and 8.82, 6.23 and 5.39 during treatment, respectively. Average SUVmax at baseline was 14.68 in responders to CPI and 8.28 in non-responders (P=0.006). On treatment SUVmax was 10.93 in responders to CPI and 8.22 in non-responders (P=0.19). A strong correlation between CD8 expression in baseline tissue and normalized SUVmean was observed (r=0.77; 95%CI 0.53-0.91). Conclusions: To our knowledge, this is the first series in RCC to demonstrate that functional imaging of immune cells (here, CD8s) may segregate response to CPIs, with responders having a higher baseline SUV and a larger decrement in SUV with therapy. Our results are bolstered by a significant correlation between tissue and imaging CD8 expression. Larger studies are underway to validate this noninvasive strategy. Clinical trial information: NCT03802123 .

Inatorial forecasting method considering macro and micro characteristics of chaotic traffic flow

Traffic flow prediction is an effective strategy to assess traffic conditions and alleviate traffic congestion. Influenced by external non-stationary factors and road network structure, traffic flow sequences have macro spatiotemporal characteristics and micro chaotic characteristics. The key to improving the model prediction accuracy is to fully extract the macro and micro characteristics of traffic flow time sequences. However, traditional prediction model by only considers time features of traffic data, ignoring spatial characteristics and nonlinear characteristics of the data itself, resulting in poor model prediction performance. In view of this, this research proposes an intelligent combination prediction model taking into account the macro and micro features of chaotic traffic data. Firstly, to address the problem of time-consuming and inefficient multivariate phase space reconstruction by iterating nodes one by one, an improved multivariate phase space reconstruction method is proposed by filtering global representative nodes to effectively realize the high-dimensional mapping of chaotic traffic flow. Secondly, to address the problem that the traditional combinatorial model is difficult to adequately learn the macro and micro characteristics of chaotic traffic data, a combination of convolutional neural network (CNN) and convolutional long short-term memory (ConvLSTM) is utilized for capturing nonlinear features of traffic flow more comprehensively. Finally, to overcome the challenge that the combined model performance degrades due to subjective empirical determined network parameters, an improved lightweight particle swarm is proposed for improving prediction accuracy by optimizing model hyperparameters. In this paper, two highway datasets collected by the Caltrans Performance Measurement System (PeMS) are taken as the research objects, and the experimental results from multiple perspectives show that the comprehensive performance of the method proposed in this research is superior to those of the prevalent methods.

Correlation Study of Temporal Climate Networks Based on Weighted Cumulative Node Evaluation

In order to systematically analyze the characteristics of climate change in China in recent years, this paper selects the data of 6 climate factors from China meteorological stations during 1984-2016 for 33 years. With the help of complex network theory, the representative climate nodes in China are determined by node importance evaluation method with the power to accumulate intermediate centrality. Multiple single-factor temporal static and temporal dynamic climate network models are constructed to explore the correlation of representative node networks of Climate in China. The results show that the temperature network has the strongest correlation. The temporal static network has the weakest correlation with precipitation network, while the temporal dynamic network has the weakest correlation with wind velocity network and shows a weak fluctuation downward trend.

Optimal vs rotation heuristics in the role of cluster-head for routing in IoT constrained devices

Wireless Sensor Networks (WSNs) are crucial for implementing the Internet of Things (IoT) vision. A WSN can include distributed devices that can be battery powered, have a small amount of memory, have limited CPU processing capabilities and limited transmission range. WSNs are categorised into two main types that are homogeneous and heterogeneous. Homogeneous WSNs are composed of nodes that are all equal while heterogeneous ones are composed of nodes that can have different transmission rate and different initial energy. Collecting data in an energy efficient manner is one of the main goals when building wireless sensor networks since devices are battery powered and battery replacement can be difficult or impossible to be performed. Clustering protocols are one of the main approaches that have been used in order to collect data in an energy efficient way. A clustering protocol groups nodes into a set of clusters. Each cluster has a representative node that is referred to as Cluster Head (CH). This collects data from its cluster members and forwards them to an external Base Station, possibly in a multi-hop way among cluster heads. A rotation strategy for electing the cluster head is often used together with clustering in order to prolong the network lifetime. Rotation eliminates the overhead traffic that is needed for leader election and cluster formation since the old cluster heads directly designate new ones. In this work, we describe an Optimum Rotation Scheduling (ORS) that uses Integer Linear Programming in order to find the optimum rotation strategy. ORS assumes the WSN clusters are already formed by using some clustering protocol. A novel integer linear programming formulation is then used in order to define a cluster head rotation that produces the optimum cluster lifetime. Comparisons with existing heuristics and the provided optimum are then shown and discussed by means of extended simulations involving both homogeneous and heterogeneous WSNs.