Minimum Spanning Tree Algorithm Research Articles

Minimum spanning tree analysis of EEG resting-state functional networks in schizophrenia

Schizophrenia is a serious and complex mental disease, known to be associated with various subtle structural and functional deviations in the brain. Recently, increased attention is given to the analysis of brain-wide, global mechanisms, strongly altering the communication of long-distance brain areas in schizophrenia. Data of 32 patients with schizophrenia and 28 matched healthy control subjects were analyzed. Two minutes long 64-channel EEG recordings were registered during resting, eyes closed condition. Average connectivity strength was estimated with Weighted Phase Lag Index (wPLI) in lower frequencies: delta and theta, and Amplitude Envelope Correlation with leakage correction (AEC-c) in higher frequencies: alpha, beta, lower gamma and higher gamma. To analyze functional network topology Minimum Spanning Tree (MST) algorithms were applied. Results show that patients have weaker functional connectivity in delta and alpha frequency bands. Concerning network differences, the result of lower diameter, higher leaf number, and also higher maximum degree and maximum betweenness centrality in patients suggest a star-like, and more random network topology in patients with schizophrenia. Our findings are in accordance with some previous findings based on resting-state EEG (and fMRI) data, suggesting that MST network structure in schizophrenia is biased towards a less optimal, more centralized organization.

Priority queues with decreasing keys

A priority queue stores a multiset of items, each item being a 〈key,value〉 pair, and supports the insertion of a new item and extraction of an item with minimum key. In applications like Dijkstra's single source shortest path algorithm and Prim-Jarník's minimum spanning tree algorithm, the key of an item can decrease over time. Usually this is handled by either using a priority queue supporting the deletion of an arbitrary item or a dedicated DecreaseKey operation, or by inserting the same item multiple times but with decreasing keys.In this paper we study what happens if the keys associated with the items in a priority queue can decrease over time without informing the priority queue, and how such a priority queue can be used in Dijkstra's algorithm. We show that binary heaps with bottom-up insertions fail to report items with unchanged keys in correct order, while binary heaps with top-down insertions report items with unchanged keys in correct order. Furthermore, we show that skew heaps, leftist heaps, and priority queues based on linking the roots of heap-ordered trees, like pairing heaps, binomial queues and Fibonacci heaps, work correctly with decreasing keys without any modifications. Finally, we show that the post-order heap by Harvey and Zatloukal, a variant of a binary heap with amortized constant time insertions and amortized logarithmic time deletions, works correctly with decreasing keys and is a strong contender for an implicit priority queue supporting decreasing keys in practice.

Learning Ultrametric Trees for Optimal Transport Regression

Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the space. However, measures supported on trees admit a closed-form optimal transport that can be computed in linear time. In this paper, we aim to find an optimal tree structure for a given discrete metric space so that the tree-Wasserstein distance approximates the optimal transport distance in the original space. One of our key ideas is to cast the problem in ultrametric spaces. This helps us optimize over the space of ultrametric trees --- a mixed-discrete and continuous optimization problem --- via projected gradient decent over the space of ultrametric matrices. During optimization, we project the parameters to the ultrametric space via a hierarchical minimum spanning tree algorithm, equivalent to the closest projection to ultrametrics under the supremum norm. Experimental results on real datasets show that our approach outperforms previous approaches (e.g. Flowtree, Quadtree) in approximating optimal transport distances. Finally, experiments on synthetic data generated on ground truth trees show that our algorithm can accurately uncover the underlying trees.

Robust ambiguity datum for real-time GNSS satellite integer clock estimation

With the capability for single-receiver AR (Ambiguity Resolution), real-time GNSS (Global Navigation Satellite System) satellite integer clock has been the research hotspot of GNSS community in the past decade. Robust ambiguity datum is one prerequisite for high-quality integer clock. In this paper, with undifferenced AR model derived, a robust ambiguity datum definition method is proposed to isolate the signal biases from the integer ambiguity. Firstly, based on the ambiguity graph, the ambiguity datum is selected with the minimum spanning tree algorithm. Secondly, the ambiguity datum is transferred to the subsequent epochs through signal bias connection. Moreover, additional datum ambiguities are introduced to accommodate the arising of receiver and satellite in real-time circumstance. With the combination of ambiguity graph and signal bias, the efficient definition and smooth transition of ambiguity datum are assured for the real-time processing. To validate the approach, simulated real-time integer clock estimation for GPS/Galileo/BDS-3 satellites are conducted with one-month (January 2022) data from about 100 global IGS (International GNSS Service) network stations. Experiments show that the proposed robust ambiguity datum can produce accurate real-time integer clock. The average WL (Wide-Lane) and NL (Narrow-Lane) fixed rates exceed 99 % and 95 %, respectively, for most of the GPS/Galileo satellites. While comparable WL fixed rate is achieved for the BDS-3 satellites, the NL fixed rate is about 5 % lower as a result of poor orbit quality and imperfect measurement model. With eclipsing satellites excluded, the standard deviations between real-time integer clock and post-processed reference clock reach 0.018 ns and 0.016 ns for the GPS and Galileo constellations, respectively, which are 28 % and 24 % smaller than those of corresponding float clocks. In contrast, the standard deviations of float and integer clocks are similar for the BDS-3 constellation. Further improvements on the background models, including unconservative force modeling, satellite attitude modeling and antenna calibration are required to achieve ultimate accuracy, especially for the BDS-3 satellites.

Robust optimization of a closed-loop supply chain network based on an improved genetic algorithm in an uncertain environment

Aiming at the network structure design problems of facility location, path planning, and flow distribution in an e-commerce closed-loop supply chain network under an uncertain environment, the uncertainties of both the forward and reverse logistics demands and the impact of facility disruptions are analyzed. A robust optimization model is established using the robust peer-to-peer optimization method. An algorithm is designed that combines the minimum spanning tree algorithm with a two-layer adaptive genetic algorithm (Prim-DMGA) to solve the model. The results show that the Prim-DMGA not only requires less computation time, but also generates solutions of higher quality. In addition, the application of the robust optimization model reduces the adverse effects of uncertain factors on the e-commerce closed-loop supply chain network, thereby improving its robustness.

Optimization of subsea production facilities layout based on cluster manifold system considering seabed topography

High investment in deep-water development highlights the importance of optimizing the subsea layout, a properly optimized subsea production system reduces costs and contributes to production performance. Aiming at the minimum total construction cost of a subsea cluster manifold system, an integrated mathematical model considering the combination of subsea well grouping, cluster manifold layout, connection relationships, pipe routes and seabed topography is developed in this study. A modified adaptive particle swarm optimization (MAPSO) algorithm coupled with A-star algorithm, clustering algorithm and minimum spanning tree algorithm is used to solve the model by using a newly proposed process. The feasibility and practicality of the model is verified by designing the layout of a deep-water oil field, and the influence of manifold number and seabed topography is demonstrated by the difference in suggested cost. The model provides a new method which can be used to estimate costs more reliably.

The comparison of three MST algorithms

The minimum spanning tree, connecting all the nodes of a connected, weighted graph with the minimum possible total edge weight, is a fundamental concept of graph theory. Thus, how to find the minimum spanning tree (MST) with higher efficiency appears to be crucial. Three kinds of algorithms for this problem have already been developed: Kruskal, Prim, Boruvka. In order to make readers have a better understanding of the three algorithms in the process of studying and teaching, this paper uses the method of comparing to indicate the differences and commonalities between these three algorithms, draws a conclusion afterwards, and points out the most suitable situations to apply them in the end: Kruskals algorithm is suitable in sparse graphs while Prims algorithm and Boruvkas algorithm are suitable in dense graphs.

Effects of visual-electrotactile stimulation feedback on brain functional connectivity during motor imagery practice

The use of neurofeedback is an important aspect of effective motor rehabilitation as it offers real-time sensory information to promote neuroplasticity. However, there is still limited knowledge about how the brain’s functional networks reorganize in response to such feedback. To address this gap, this study investigates the reorganization of the brain network during motor imagery tasks when subject to visual stimulation or visual-electrotactile stimulation feedback. This study can provide healthcare professionals with a deeper understanding of the changes in the brain network and help develop successful treatment approaches for brain–computer interface-based motor rehabilitation applications. We examine individual edges, nodes, and the entire network, and use the minimum spanning tree algorithm to construct a brain network representation using a functional connectivity matrix. Furthermore, graph analysis is used to detect significant features in the brain network that might arise in response to the feedback. Additionally, we investigate the power distribution of brain activation patterns using power spectral analysis and evaluate the motor imagery performance based on the classification accuracy. The results showed that the visual and visual-electrotactile stimulation feedback induced subject-specific changes in brain activation patterns and network reorganization in the alpha band. Thus, the visual-electrotactile stimulation feedback significantly improved the integration of information flow between brain regions associated with motor-related commands and higher-level cognitive functions, while reducing cognitive workload in the sensory areas of the brain and promoting positive emotions. Despite these promising results, neither neurofeedback modality resulted in a significant improvement in classification accuracy, compared with the absence of feedback. These findings indicate that multimodal neurofeedback can modulate imagery-mediated rehabilitation by enhancing motor-cognitive communication and reducing cognitive effort. In future interventions, incorporating this technique to ease cognitive demands for participants could be crucial for maintaining their motivation to engage in rehabilitation.

Clonal aggregation of fluconazole-resistant Candida tropicalis isolated from sterile body fluid specimens from patients in Hefei, China.

Candida tropicalis, a human conditionally pathogenic yeast, is distributed globally, especially in Asia-Pacific. The increasing morbidity and azole resistance of C. tropicalis have made clinical treatment difficult. The correlation between clonality and antifungal susceptibility of clinical C. tropicalis isolates has been reported. To study the putative correlation in C. tropicalis isolated from normally sterile body fluid specimens and explore the distinct clonal complex (CC) in Hefei, 256 clinical C. tropicalis isolates were collected from four teaching hospitals during 2016-2019, of which 30 were fluconazole-resistant (FR). Genetic profiles of 63 isolates, including 30 FR isolates and 33 fluconazole-susceptible (FS) isolates, were characterized using multilocus sequence typing (MLST). Phylogenetic analysis of the data was conducted using UPGMA (unweighted pair group method with arithmetic averages) and the minimum spanning tree algorithm. MLST clonal complexes (CCs) were analyzed using the goeBURST package. Among 35 differentiated diploid sequence types (DSTs), 16 DSTs and 1 genotype were identified as novel. A total of 35 DSTs were assigned to five major CCs based on goeBURST analysis. CC1 (containing DST376, 505, 507, 1221, 1222, 1223, 1226, and 1229) accounted for 86.7% (26/30) of the FR isolates. However, the genetic relationships among the FS isolates were relatively decentralized. The local FR CC1 belongs to a large fluconazole non-susceptible CC8 in global isolates, of which the putative founder genotype was DST225. The putative correlation between MLST types and antifungal susceptibility of clinical C. tropicalis isolates in Hefei showed that DSTs are closely related to FR clones.

CMSTR: A Constrained Minimum Spanning Tree Based Routing Protocol for Wireless Sensor Networks

How to extend the network lifetime with given limited energy budget is always one of the main concerns in Wireless Sensor Networks (WSNs). However, imbalanced energy consumption and overlong intra-cluster communication paths are prevalent in the hierarchical routing protocols, which shortens the network lifetime inevitably. To this end, an energy-efficient routing Protocol based on Constrained Minimum Spanning Tree (CMSTR) is proposed in this paper. To be specific, a new multichain routing scheme to balance the energy consumption for intra-cluster communications is presented. Based on the multichain routing scheme, the problem of establishing intra-cluster routing is transformed into a shortest Hamiltonian path problem on the basis of a graph-theoretic analysis model, which is solved through a Constrained Minimum Spanning Tree (CMST) algorithm proposed in this paper, with the aim to obtain the initial path for intra-cluster communications. In order to shorten the initial path length to obtain higher energy-efficient chain routes, a Neighbor Node Replacement (NNR) algorithm and a Link Intersection Detection and Elimination (LIDE) algorithm are proposed, in which the problem of potential long links and intersections is to be effectively alleviated. With shorter chain routes, unnecessary intra-cluster communication energy depletion can be reduced accordingly. In order to evaluate the performance of CMSTR, extensive simulation experiments are conducted. The results show that CMSTR can greatly prolong the network lifetime with regard to the metrics of FND and HND. To be specific, compared with LEACH, R-LEACH, and DCMSTR, the value of FND increased by 800%, 540% and 57%, that of HND increased by 322%, 286% and 22%, and overall network lifetime (AND) increased by 29%, 10% and 5%, respectively. Besides, CMSTR has a stable and lowest packet loss percentage (0.4%). In summary, CMSTR has excellent performance in terms of energy efficiency and network stability.

Minimum Spanning Tree Method for Sparse Graphs

The minimum spanning tree (MST) is widely used in planning the most economical network. The algorithm for finding the MST of a connected graph is essential. In this paper, a new algorithm for finding MST is proposed based on a deduced theorem of MST. The algorithm first sorts the edges in the graph according to their weight, from large to small. Next, on the premise of ensuring the connectivity of the graph, it deletes the edges in this order until the number of edges of the graph is equal to the number of vertexes minus 1. Finally, the remaining graph is an MST. This algorithm is equivalent to an inverse Kruskal algorithm. For sparse graphs, the proposed algorithm has higher efficiency than the Kruskal algorithm. Experiments and analysis verify the effectiveness of the algorithm proposed in this paper. The algorithm provides a better choice for finding the MST of the sparse graph.

A K-Means Clustering and the Prim’s Minimum Spanning Tree-Based Optimal Picking-List Consolidation and Assignment Methodology for Achieving the Sustainable Warehouse Operations

Rapid industrialization has caused the concentration of greenhouse gases in the atmosphere to increase rapidly, leading to drastic global climate changes and ecological degradation. To establish a sustainable supply chain for consumer electronic products, this study focuses on warehouse operations and develops a K-means clustering and Prim’s minimum spanning tree-based optimal picking-list consolidation and assignment methodology. Compact camera modules are used to demonstrate and verify the effectiveness of this methodology. This methodology can be divided into two parts. First, the K-means clustering method is applied to conduct a picking-list consolidation analysis to create an optimal picking-list consolidation strategy for sustainable warehouse operations. Second, the most similar picking lists in each cluster are connected using Prim’s minimum spanning tree algorithm to generate the connected graph with the minimum spanning tree so as to establish a picking-list assignment strategy for sustainable warehouse operations. In this case study, this to-be model substantially reduced the traveling distance of the electric order-picking trucks within a warehouse and increased the picking efficiency to diminish the carbon emissions toward a sustainable supply chain.

On the Spatial Distribution of 13CO Structures within 12CO Molecular Clouds

We look into the 2851 12CO molecular clouds harboring 13CO structures to reveal the distribution of the projected angular separations and radial velocity separations between their internal 13CO structures. The projected angular separations are determined using the minimal spanning tree algorithm. We find that ∼50% of the angular separations fall in a narrow range of ∼3′–7′ with a median of ∼5′, and the corresponding radial velocity separations mainly range from ∼0.3 to 2.5 km s−1. The mean and standard deviation of the angular separations of the internal 13CO structures within 12CO clouds appear to be universal, independent of the 12CO cloud angular areas and the counts of their internal 13CO structures. We also reveal a scaling relation between the 12CO cloud angular area and its harbored 13CO structure count. These results suggest there is a preferred angular separation between 13CO structures in these 12CO clouds, considering the distance effects. According to that, we propose an alternative picture for the assembly and destruction of molecular clouds: there is a fundamental separation for the internal structures of molecular clouds, the build-up and destruction of molecular clouds proceeds under this fundamental unit.

Relay node placement in wireless sensor network for manufacturing industry

Relay nodes are necessary to maintain scalability and increase longevity as the number of manufacturing industrial sensors grows. In a fixed-budget circumstance, however, the cost of purchasing the bare minimum of relay nodes to connect the network may exceed the budget. Although it is hard to establish a network that connects all sensor nodes, in this case, a network with a high level of connection is still desirable. This paper proposes two metrics for determining the connectedness of a disconnected graph of sensor nodes and determining the optimum deployment method for relay nodes in a network with the highest connectedness while staying within a budget restriction. The metrics are the number of connected graph components and the size of the most significant connected graph component. Prim's algorithm and the approximation minimum spanning tree algorithm are applied to construct a disconnected graph and discover the best relay node placement to solve these two criteria. Compared to the other metrics, simulation findings suggest that prioritizing the most significant connected components in the disconnected graph can yield superior outcomes by deploying the fewest number of relay nodes while retaining the connectedness of the graph.

FL-SDUAN: A Fuzzy Logic-Based Routing Scheme for Software-Defined Underwater Acoustic Networks

In underwater acoustic networks, the accurate estimation of routing weights is NP-hard due to the time-varying environment. Fuzzy logic is a powerful tool for dealing with vague problems. Software-defined networking (SDN) is a promising technology that enables flexible management by decoupling the data plane from the control plane. Inspired by this, we proposed a fuzzy logic-based software-defined routing scheme for underwater acoustic networks (FL-SDUAN). Specifically, we designed a software-defined underwater acoustic network architecture. Based on fuzzy path optimization (FPO-MST) and fuzzy cut-set optimization (FCO-MST), two minimum spanning tree algorithms under different network scales were proposed. In addition, we compared the proposed algorithms to state-of-the-art methods regarding packet delivery rate, end-to-end latency, and throughput in different underwater acoustic network scenarios. Extensive experiments demonstrated that a trade-off between performance and complexity was achieved in our work.

Midrapidity cluster formation in heavy-ion collisions

We study the production of clusters and hypernuclei at midrapidity employing the Parton-Hadron- Quantum-Molecular-Dynamics (PHQMD) approach, a microscopic n-body transport model based on the QMD propagation of the baryonic degrees of freedom with density dependent 2-body potential interactions. In PHQMD the cluster formation occurs dynamically, caused by the interactions. The clusters are recognized by the Minimum Spanning Tree (MST) algorithm. We present the PHQMD results for cluster and hypernuclei formation in comparison with the available experimental data at relativistic energies. PHQMD allows to study the time evolution of formed clusters and the origin of their production, which helps to understand how such weakly bound objects are formed and survive in the rather dense and hot environment created in heavy-ion collisions. It offers therefore an explanation of the ’ice in the fire’ puzzle. To investigate whether this explanation of the ’ice in the fire’ puzzle applies only to the MST results we study also the deuterons production by coalescence. We embed MST and coalescence in the PHQMD and UrQMD transport approaches in order to obtain model independent results. We find that both clustering procedures give very similar results for the deuteron observables in the UrQMD as well as in the PHQMD environment. This confirms that our solution for the ’ice in the fire’ puzzle is common to MST and coalescence and independent of the transport approach.

Optimizing the University Student Advising Process through Weighted Minimum Spanning Tree Algorithm

Optimizing the University Student Advising Process through Weighted Minimum Spanning Tree Algorithm

Distribution network reconfiguration and reactive power compensation using a hybrid Simulated Annealing – Minimum spanning tree algorithm

Change of the climate, environmental pollution and lack of classical energy sources forced many countries to address renewables. In modern strategies of smart distribution network reconfiguration should be applied in order to minimize power losses and economic costs. Also, capacitors switching (placement of shunt capacitors) and presence of distribution generation are always incorporated in modern networks. Further, On Load Tap Changer in the supplying substation has to be used. Simulated Annealing and Minimum spanning tree algorithms work separately in order to find the best appropriate solution. The main goals are minimization of power losses and costs. In addition, many constraints are attended to find the hourly reconfiguration and capacitor banks position. Distributed generators involve both wind generators and solar panels. Two methods described in literature are mixed and implemented for locating fixed nodes for distributed generators. Gauss and Weibull changing nodal loads and wind generators output respectively, as well as daily load curves for working and weekend day with insolation of solar panels are included in analysis. Per unit load diagrams are determined according to real one-year measurement results in one substation in Belgrade, Serbia. IEEE 69 bus network is analyzed. The main contribution of exposed research is near optimal solution for wide time range, realistic network operation/planning forecast (stochastic variation of consumption and production on hour basis) with satisfaction of all technical constraints that are minimum and maximum nodal voltages, limiting feeder’s capacities and not-overcompensation of the network, accompanied with elaborate economic background.

An Energy Efficient Load Balancing Tree-Based Data Aggregation Scheme for Grid-Based Wireless Sensor Networks

A wireless sensor network (WSN) consists of a very large number of sensors which are deployed in the specific area of interest. A sensor is an electronic device equipped with a small processor and has a small-capacity memory. The WSN has the functions of low cost, easy deployment, and random reconfiguration. In this paper, an energy-efficient load balancing tree-based data aggregation scheme (LB-TBDAS) for grid-based WSNs is proposed. In this scheme, the sensing area is partitioned into many cells of a grid and then the sensor node with the maximum residual energy is elected to be the cell head in each cell. Then, the tree-like path is established by using the minimum spanning tree algorithm. In the tree construction, it must meet the three constraints, which are the minimum energy consumption spanning tree, the network depth, and the maximum number of child nodes. In the data transmission process, the cell head is responsible for collecting the sensing data in each cell, and the collected data are transmitted along the tree-like path to the base station (BS). Simulation results show that the total energy consumption of LB-TBDAS is significantly less than that of GB-PEDAP and PEDAP. Compared to GB-PEDAP and PEDAP, the proposed LB-TBDAS extends the network lifetime by more than 100%. The proposed LB-TBDAS can avoid excessive energy consumption of sensor nodes during multi-hop data transmission and can also avoid the hotspot problem of WSNs.

A Coordination Optimization Method for Load Shedding Considering Distribution Network Reconfiguration

Load shedding control is an emergency control measure to maintain the frequency stability of the power system. Most of the existing load shedding methods use the extensive form of directly cutting off the outlet of the substation, featuring low control accuracy and high control cost. A network reconfiguration technique can adjust the topology of the distribution network and offers more optimization space for load shedding control. Therefore, this paper proposes a reconfiguration–load shedding coordination optimization scheme to reduce the power loss caused by load shedding control. In the proposed method, a load shedding mathematical optimization model based on distribution network reconfiguration is first established. The tie switches and segment switches in the distribution network are used to perform the reconfiguration of the distribution network, and the load switches are adopted to realize the load shedding. To improve the solving efficiency of the model, a solving strategy that combined a minimum spanning tree algorithm with an improved genetic algorithm is trailed to address the nonlinear and nonconvex terms. The application of the proposed method and model are finally verified via the IEEE 33 bus system, and the advantages in reducing the loss cost and the number of outage users are accordingly proven.