Minimum Spanning Research Articles

GAL: Graph-Induced Adaptive Learning for Weakly Supervised 3D Object Detection

Weakly Supervised 3D Object Detection (WS3DOD) aims to perform 3D object detection with little reliance on 3D labels, which greatly reduces the cost of 3D annotations. In recent literature, the pseudo-label-based approach brings impressive performance, which generates 3D pseudo-labels from 2D bounding boxes. Despite their success, two key issues remain unresolved that reduce the quality of 3D pseudo-labels: 1) the existing local object locating algorithm can not capture complete clusters of points globally, and 2) the existing algorithm can not capture sparse points caused by the unevenly distributed points obtained by LiDAR cameras. Hence, we propose GAL, a Graph-induced Adaptive Learning algorithm, to generate 3D pseudo-labels. First, we propose the Cluster Locating algorithm based on the Minimum Spanning Tree (MST) to globally locate the objects, which can leverage the characteristic that points inside an object are compact while points between objects are discrete. Second, we propose a density-guided adaptive learning algorithm to optimise the Cluster Locating algorithm, named Cuboid Drift. Cuboid Drift considers the inhomogeneous distribution of reflected points on different reflective surfaces of LiDAR imaging. Finally, 3D pseudo-labels generated by GAL are leveraged to train 3D detectors. Extensive experiments on the challenging <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">KITTI </i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DAIR-V2X-V</i> dataset demonstrate that GAL without 3D labels can be comparable with strongly supervised approaches and outperforms the previous state-of-the-art WS3DOD methods. Moreover, our method saves 88% of the time spent on pseudo-label generation.

Retracted: COVID-19 Infection Structure Analysis Based on Minimum Spanning Tree Visualization in the Kingdom of Saudi Arabia Regions

Retracted: COVID-19 Infection Structure Analysis Based on Minimum Spanning Tree Visualization in the Kingdom of Saudi Arabia Regions

On the complexity of the Cable-Trench Problem

The Cable-Trench Problem (CTP) is a common generalization of the Single-Source Shortest Paths Problem (SSSP) and the Minimum Spanning Tree Problem (MST): given an edge-weighted graph with a special root vertex and parameters τ,γ≥0, the goal is to find a spanning tree that minimizes the total edge costs plus the total cost of the paths from each vertex to the root, scaled by τ and γ, respectively. While it is well known that both SSSP and MST can be solved in polynomial time, CTP is NP-hard. We show that computing an approximate solution with factor less than 1.000475 is NP-hard, thus ruling out a polynomial-time approximation scheme, unless P=NP.We also consider the more general Steiner Cable-Trench Problem (SCTP), for which only a given subset of terminal vertices must be spanned by a solution. The tree might include non-terminal vertices, known as Steiner vertices, although only paths from terminals to the root are considered in the total cost. For this problem, we present a (2.88+ϵ)-approximation based on a counting argument, for any ϵ>0; also, we give a simple parameterized algorithm with the number of terminals as parameter.

Simulated Annealing is a Polynomial-Time Approximation Scheme for the Minimum Spanning Tree Problem

We prove that Simulated Annealing with an appropriate cooling schedule computes arbitrarily tight constant-factor approximations to the minimum spanning tree problem in polynomial time. This result was conjectured by Wegener (Automata, Languages and Programming, ICALP, Berlin, 2005). More precisely, denoting by n, m, w_{max }, and w_{min } the number of vertices and edges as well as the maximum and minimum edge weight of the MST instance, we prove that simulated annealing with initial temperature T_0 ge w_{max } and multiplicative cooling schedule with factor 1-1/ell , where ell = omega (mnln (m)), with probability at least 1-1/m computes in time O(ell (ln ln (ell ) + ln (T_0/w_{min }) )) a spanning tree with weight at most 1+kappa times the optimum weight, where 1+kappa = frac{(1+o(1))ln (ell m)}{ln (ell ) -ln (mnln (m))}. Consequently, for any epsilon >0, we can choose ell in such a way that a (1+epsilon )-approximation is found in time O((mnln (n))^{1+1/epsilon +o(1)}(ln ln n + ln (T_0/w_{min }))) with probability at least 1-1/m. In the special case of so-called (1+epsilon )-separated weights, this algorithm computes an optimal solution (again in time O( (mnln (n))^{1+1/epsilon +o(1)}(ln ln n + ln (T_0/w_{min })))), which is a significant speed-up over Wegener’s runtime guarantee of O(m^{8 + 8/epsilon }). Our tighter upper bound also admits the result that in some situations a hybridization of simulated annealing and the {(1 + 1)} EA can lead to stronger runtime guarantees than either algorithm alone.

The dynamics of psychological attributes and symptomatic comorbidity of depression in children and adolescents

PurposeThis investigation aimed to explore attribute dynamics and symptomatic comorbidity of depression with internalizing, externalizing, and other personal–contextual problems in children and adolescents from a network analysis.MethodsWe tested an attribute network of regularized partial correlations, standard and alternative centrality measures, and comorbidity bridge symptoms according to centrality bridge measures.ResultsRegularized partial correlation network and a centrality measures graph shown the prominent position of social problems and anxiety–depression. Minimum spanning tree (MST) found a hierarchical dynamics between attributes where mixed anxiety–depression was identified as the core and the other attributes were hierarchically connected to it by being positioned in six branches that are differentiated according to their theoretical contents. The most central connections are established with the attributes of their own community or theoretical groups, and 37 bridge symptoms were identified in all networks.ConclusionsA significant role of mixed anxiety depression as an activator and intermediary of psychopathologies was supported as a central attribute of internalizing problems. Aggressive behavior as part of the broad externalizing dimension was one of the constructs that most intensively activate the network, and social problems were also distinguished as a relevant factor not only in terms of connections and central attributes but also in terms of bridge symptoms and comorbidity. This framework extends to the study of symptomatic “comorbidity.”

Note: Demonstrating analytics in a low-tech context–truck-routing for solid-waste collection in an Indian metropolis

This paper describes an approach to introducing analytics through various algorithms and applications to users in a low-tech environment as a first step toward understanding such a context. The South Delhi Municipal Corporation (SDMC) of New Delhi, India, have partitioned their collection points into “wards” or clusters, each served by a dedicated truck depot and manually routing trucks for solid waste collection within each ward, with the waste from all wards going to a single landfill. To demonstrate analytics in tactical planning, we implemented the nearest neighbor algorithm mimicking the manual process to provide the baseline cost. Thus, we presented two very different vehicle routing algorithms: (1) a simple but fast revised nearest neighbor algorithm that decreased the baseline total routing cost by 1.57 % and (2) an optimal but time-intensive algorithm using a mixed-integer-linear programming model, which decreased the total cost by 4.05 %. To demonstrate strategic planning, we tested the efficacy of the cluster structure of collection points by comparing its total routing cost (using the revised nearest neighbor algorithm) to that of other partitions obtained with Minimum Spanning Tree (MST) and K-medoids clustering. The existing wards provided a lower waste pickup cost than the alternative clusters we created, showing SDMC that their existing ward structure was sound.

Minimum spanning tree niching-based differential evolution with knowledge-driven update strategy for multimodal optimization problems

Multimodal optimization problems (MMOPs) aim to simultaneously locate as many global optima as possible with high accuracy. Recently, many niching strategies have been wildly used in evolutionary algorithms to solve MMOPs due to the advantage of maintaining the diversity of population. However, most multimodal algorithms are sensitive to the niching parameters and lack effective methods to update the “stagnant individuals”, including individuals that have trapped into local optima or converged to the same optima. In this paper, a minimum spanning tree niching-based differential evolution (TNDE) with knowledge-driven update (KDU) strategy is proposed to better solve the above challenges, where the “knowledge” includes historical evolutionary information, fitness distribution information, and individual distribution information. In TNDE, a minimum spanning tree niching (MSTN) strategy is proposed to adaptively divide the population, which can adjust the number of niches dynamically. Besides, the KDU strategy is proposed to utilize the knowledge to locate and update stagnant individuals. Lastly, an improved differential evolution with local stage-based mutation (LSM) and directional guidance selection (DGS) strategies is proposed to accelerate convergence and refine the accuracy of solutions, respectively. The comparison results with 16 state-of-the-art algorithms on CEC’2013 show that TNDE achieves significant advantages on high-dimensional problems or problems with many global optima.

Image Subset Union for Compressed Image Sets in Cloud Servers

Image deletion and image insertion, the current commonly used two kinds of image set management, refer to removing compressed images from and adding new photos to a compressed image set, respectively. However, they do not deal with well the problem of the combination of images selected from multiple compressed image sets. To address this issue, in this paper we first propose an image subset union algorithm for compressed image sets. Image subset union aims to integrate image subsets derived from multiple compressed image sets into a new compressed image set. First, we put forward a way to identify the root vertex candidate of the new compressed image set. Second, we classify all the images of image subsets into three categories: images needed to be re-encoded, images needed to be only decoded, and images unneeded to be re-encoded or decoded. Third, we also employ minimum spanning tree production, a proposed vertex layer candidate assignment method, depth- and subtree-constrained minimum spanning tree generation, as well as image re-encoding to build the new compressed image set. Experimental results show that our proposed algorithm can effectively accomplish image subset union with low complexity.

Similar connectivity of gut microbiota and brain activity networks is mediated by animal protein and lipid intake in children from a Mexican indigenous population.

The gut microbiota-brain axis is a complex communication network essential for host health. Any long-term disruption can affect higher cognitive functions, or it may even result in several chronic neurological diseases. The type and diversity of nutrients an individual consumes are essential for developing the gut microbiota (GM) and the brain. Hence, dietary patterns might influence networks communication of this axis, especially at the age that both systems go through maturation processes. By implementing Mutual Information and Minimum Spanning Tree (MST); we proposed a novel combination of Machine Learning and Network Theory techniques to study the effect of animal protein and lipid intake on the connectivity of GM and brain cortex activity (BCA) networks in children from 5-to 10 years old from an indigenous community in the southwest of México. Socio-ecological conditions in this nonwestern lifestyle community are very homogeneous among its inhabitants but it shows high individual heterogeneity in the consumption of animal products. Results suggest that MST, the critical backbone of information flow, diminishes under low protein and lipid intake. So, under these nonwestern regimens, deficient animal protein and lipid consumption diets may significantly affect the GM-BCA connectivity in crucial development stages. Finally, MST offers us a metric that unifies biological systems of different nature to evaluate the change in their complexity in the face of environmental pressures or disturbances. Effect of Diet on gut microbiota and brain networks connectivity.

A pairwise mixing model with kernel constraint and its appraisal in transported PDF simulations of ethylene flames

Modeling micro-mixing remains a primary challenge for the transported probability density function (TPDF) method. In this study, the pairwise mixing with kernel constraint (KerM) model is proposed and evaluated in TPDF simulations of a turbulent non-premixed ethylene flame. The new model features controllable localness by selecting mixing particle pairs with a probability that depends on their distance in composition space, normalized by a characteristic kernel size. To evaluate the model in a controlled setting, TPDF simulations were carried out with the mean velocity, turbulent diffusivity and scalar mixing frequencies extracted from a direct numerical simulation (DNS) dataset. The predictions of the mean statistics and the conditional PDFs illustrate that the KerM model exhibits asymptotic behavior to the modified Curl (MC) and the Euclidean minimum spanning trees (EMST) model, respectively, depending on the kernel size. For the flame considered, results for KerM approach those for EMST when the kernel size is less than 0.01, while they approach those for MC when the kernel size is larger than 1.0. Given a kernel size of 0.1, KerM yields a notably better prediction of the overall combustion process than the conventional MC model. The predictions of the mean temperature and species mass fractions by KerM are similar to those by EMST, while KerM better predicts the conditional PDF of temperature than EMST that overdamps the conditional fluctuations. In addition, its complexity with the number of particles per cell is instead of O(Np2) for EMST. By incorporating different mixing timescales among species, the KerM-DD model better predicts the mean temperature field at the time instant close to local extinction than the KerM and EMST models. This work demonstrates that the KerM model, apart from being simple and robust in terms of implementation, features the advantages of being flexible in localness and being capable of incorporating differential diffusion.

Effect of electroconvulsive therapy on brain functional network in major depressive disorder

Electroconvulsive therapy (ECT) is an interventional technique capable of highly effective neuromodulation in major depressive disorder (MDD), but its antidepressant mechanism remains unclear. By recording the resting-state electroencephalogram (RS-EEG) of 19 MDD patients before and after ECT, we analyzed the modulation effect of ECT on the resting-state brain functional network of MDD patients from multiple perspectives: estimating spontaneous EEG activity power spectral density (PSD) using Welch algorithm; constructing brain functional network based on imaginary part coherence (iCoh) and calculate functional connectivity; using minimum spanning tree theory to explore the topological characteristics of brain functional network. The results show that PSD, functional connectivity, and topology in multiple frequency bands were significantly changed after ECT in MDD patients. The results of this study reveal that ECT changes the brain activity of MDD patients, which provides an important reference in the clinical treatment and mechanism analysis of MDD.

BUILDING MINIMUM SPANNING TREES BY LIMITED NUMBER OF NODES OVER TRIANGULATED SET OF INITIAL NODES

Background. The common purpose of modelling and using minimum spanning trees is to ensure efficient coverage. In many tasks of designing efficient telecommunication networks, the number of network nodes is usually limited. In terms of rational allocation, there are more possible locations than factually active tools to be settled to those locations.&#x0D; Objective. Given an initial set of planar nodes, the problem is to build a minimum spanning tree connecting a given number of the nodes, which can be less than the cardinality of the initial set. The root node is primarily assigned, but it can be changed if needed.&#x0D; Methods. To obtain a set of edges, a Delaunay triangulation is performed over the initial set of nodes. Distances between every pair of the nodes in respective edges are calculated. These distances being the lengths of the respective edges are used as graph weights, and a minimum spanning tree is built over this graph.&#x0D; Results. The problem always has a solution if the desired number of nodes (the number of available recipient nodes) is equal to the number of initially given nodes. If the desired number is lesser, the maximal edge length is found and the edges of the maximal length are excluded while the number of minimum spanning tree nodes is greater than the desired number of nodes.&#x0D; Conclusions. To build a minimum spanning tree by a limited number of nodes it is suggested to use the Delaunay triangulation and an iterative procedure in order to meet the desired number of nodes. Planar nodes of an initial set are triangulated, whereupon the edge lengths are used as weights of a graph. The iterations to reduce nodes are done only if there are redundant nodes. When failed, the root node must be changed before the desired number of nodes is changed.

The Stability of Islamic Cryptocurrencies and Copula-Based Dependence with Alternative Crypto and Fiat Currencies

Purpose — This study aims to examine Islamic cryptocurrencies and their dependency on foreign exchange markets in vine copula architecture (CD-Vine) and provide a framework for detecting complex dependence structures, risk management implications, and hedging effectiveness. Design/Methodology/Approach — This study used gold-backed cryptocurrencies and three fiat currencies. The vine copula approach was preferred because it applies several distributions and estimates complex dependencies. Hedging effectiveness was measured by constructing simulation-based portfolios optimised with DCC-t-Copula. Benford’s law and realized variance were used to determine the stability of Islamic cryptocurrencies. Findings — According to C-Vine and D-Vine copula models, paper money has a weak tail dependence with gold-backed cryptocurrencies. Only OneGram coin, whose volatility matched the risk of Bitcoin, showed zero irregularities in volume trading. The findings were robust to different estimations based on Minimum Spanning Tree and Dendrogram. Originality/Value — This is the first study to examine Islamic cryptocurrencies’ stability and the significance of hedging effectiveness on gold-backed cryptocurrencies under a copula-based approach. Research Limitations — The study did not apply time-varying vine copula. Practical Implications — The risk management perspective shows insignificant hedge effectiveness in the portfolio of fiat and gold-backed cryptocurrencies.

Cultural, creative, and complex: A computational foundation of culture-driven urban governance

Culture and creative production have an important but somewhat elusive role in urban development. None of the many conceptual paradigms that have been proposed so far to explain it has turned out entirely satisfactory. We argue that the main reason behind this failure is the implicit linear thinking that informs all these approaches: namely, the idea that a few, major drivers explain urban development through a direct, clearly readable systemic impact. Cities are complex socio-environmental systems whose functioning depends on the concurrent interaction of many different factors which cannot be reduced to the action of a few, simple causal forces. Failing to understand such complexity easily leads to dysfunctional urban governance approaches. In this paper, we analyze a database of 144 European cities as described by 58 variables belonging to different domains, as designed by a preliminary stage of the Cultural and Creative City Monitor (CCCM). Our analysis builds on innovative machine learning techniques (PST) and on the Minimum Spanning Tree (MST) representation to map the structural interdependencies between the cultural and non-cultural sectors in cities with a strong cultural policy orientation. This toolbox carries considerable potential for precision cultural policies and data-driven urban governance strategies of the future.

A solution approach to minimum spanning tree problem under fermatean fuzzy environment

In classical graph theory, the minimal spanning tree (MST) is a subgraph with no cycles that connects each vertex with minimum edge weights. Calculating minimum spanning tree of a graph has always been a common problem throughout ages. Fuzzy minimum spanning tree (FMST) is able to handle uncertainty existing in edge weights for a fuzzy graph which occurs in real world situations. In this article, we have studied the MST problem of a directed and undirected fuzzy graph whose edge weights are represented by fermatean fuzzy numbers (FFN). We focus on determining an algorithmic approach for solving fermatean fuzzy minimum spanning tree (FFMST) using the modified Prim’s algorithm for an undirected graph and modified optimum branching algorithm for a directed graph under FFN environment. Since the proposed algorithm includes FFN ranking and arithmetic operations, we use FFNs improved scoring function to compare the weights of the edges of the graph. With the help of numerical examples, the solution technique for the proposed FFMST model is described.

Genetic Diversity of Durum Wheat (Triticum turgidum L. ssp. durum, Desf) Germplasm as Revealed by Morphological and SSR Markers.

Ethiopia is considered a center of origin and diversity for durum wheat and is endowed with many diverse landraces. This research aimed to estimate the extent and pattern of genetic diversity in Ethiopian durum wheat germplasm. Thus, 104 durum wheat genotypes representing thirteen populations, three regions, and four altitudinal classes were investigated for their genetic diversity, using 10 grain quality- and grain yield-related phenotypic traits and 14 simple sequence repeat (SSR) makers. The analysis of the phenotypic traits revealed a high mean Shannon diversity index (H' = 0.78) among the genotypes and indicated a high level of phenotypic variation. The principal component analysis (PCA) classified the genotypes into three groups. The SSR markers showed a high mean value of polymorphic information content (PIC = 0.50) and gene diversity (h = 0.56), and a moderate number of alleles per locus (Na = 4). Analysis of molecular variance (AMOVA) revealed a high level of variation within populations, regions, and altitudinal classes, accounting for 88%, 97%, and 97% of the total variation, respectively. Pairwise genetic differentiation and Nei's genetic distance analyses identified that the cultivars are distinct from the landrace populations. The distance-based (Discriminant Analysis of Principal Component (DAPC) and Minimum Spanning Network (MSN)) and model-based population stratification (STRUCTURE) methods of clustering grouped the genotypes into two clusters. Both the phenotypic data-based PCA and the molecular data-based DAPC and MSN analyses defined distinct groupings of cultivars and landraces. The phenotypic and molecular diversity analyses highlighted the high genetic variation in the Ethiopian durum wheat gene pool. The investigated SSRs showed significant associations with one or more target phenotypic traits. The markers identify landraces with high grain yield and quality traits. This study highlights the usefulness of Ethiopian landraces for cultivar development, contributing to food security in the region and beyond.

Analysis and comparison of two classical greedy algorithms for minimum spanning tree

The total weight of the minimum spanning is the smallest in the connected graph. It can be used to solve many practical problems in urban life. Prims algorithm and Kruskals algorithm are greedy algorithms for solving the minimum spanning tree problem. But they make greedy choices in different ways. The paper focuses on two greedy algorithms for solving the minimum spanning tree problem. The author will evaluate each algorithms complexity and determine their most suitable condition as well. The author compares the running process of the two algorithms and analyzes the relationship between their algorithm complexity and the number of edges, which can describe the sparsity of the graphs. The result shows that Kruskals complexity is related to the number of edges, so it is better for sparse graphs. Prims complexity is related to the number of vertices, so it is better at analyzing connected graphs with lots of vertices, that is, dense graphs. As a consequence, Prims algorithm is better for dense graphs.

Efficient and Effective Directed Minimum Spanning Tree Queries

Computing directed Minimum Spanning Tree (DMST) is a fundamental problem in graph theory. It is applied in a wide spectrum of fields from computer network and communication protocol design to revenue maximization in social networks and syntactic parsing in Natural Language Processing. State-of-the-art solutions are online algorithms that compute DMST for a given graph and a root. For multi-query requirements, the online algorithm is inefficient. To overcome the drawbacks, in this paper, we propose an indexed approach that reuses the computation result to facilitate single and batch queries. We store all the potential edges of DMST in a hierarchical tree in O(n) space complexity. Furthermore, we answer the DMST query of any root in O(n) time complexity. Experimental results demonstrate that our approach can achieve a speedup of 2–3 orders of magnitude in query processing compared to the state-of-the-art while consuming O(n) index size.

MODIFIED WEIGHT MATRIX USING PRIM’S ALGORITHM IN MINIMUM SPANNING TREE (MST) APROACH FOR GSTAR(1;1) MODEL

The Generalized Space-Time Autoregressive (GSTAR) model is able to utilize modeling of both space and time simultaneously. The existence of a weight matrix is one of the aspects that established this model. The matrix illustrates the spatial impact that occurs between locations. In this research, a modified weight matrix is presented using the Minimum Spanning Tree approach of graph theory. Prim's algorithm is utilized for calculation here. Not only does the modified weight matrix depend distance, but also highlights the correlation. It makes the modified weight matrix unique. Before starting Prim's algorithm, the correlation is first utilized as an input in forming the initial graph. Following that, find the graph with the least of MST weight. Afterwards, the graph is described utilizing weight matrix, which is applied to the normalization process. Following this, the GSTAR(1;1) modelling process is carried out, beginning with estimating the parameters and then forecasting. The case study is Covid-19 cases that occurred on Java Island between July 2020 (when early Covid-19 entered Indonesia) and the beginning of January 2021. The aim of the research is to model the Covid-19 cases using modified weights and to predict the following five times. The outcome is a GSTAR(1;1) model with modified weights can captures both temporal and spatial patterns. The accuracy of the model is achieved for both the training data and the testing data by the MAPE computations, which yielded of 11.40% and 21.57%, respectively. Predictions are also obtained for each province in the next five times.

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.