Minimum Spanning Tree Research Articles

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.

Age-Optimized Multihop Information Update Mechanism on the LEO Satellite Constellation via Continuous Time-Varying Graphs

Low orbit satellite constellation as a relay network provides a possible solution for remote real-time data gathering applications, in which freshness information updates will be forwarded via dynamical intersatellite links (ISLs). Modeling by a time-varying network, this article studies minimizing Age of Information (AoI) of delivering the data through a multihop path, in particular, focusing on the effect of frequent interruptions of ISLs. Subjected to two constraints of path and effective arrival rate, the minimizing AoI problem is formulated to find a pair of optimal transmission delay and arrival rate. In particular, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}$ </tex-math></inline-formula> -approximate optimal algorithm, called a latest update routing (LUR) algorithm, is proposed with a well-designed continuous time-varying graph. Using LUR, a set of paths can be obtained with degraded transmission delay that satisfies a given arrival rate. By screening all the arrival rates satisfying the effective constraint, the maximum rate and a corresponding path set that minimizes age can be found. The simulation results verified that a degraded average AoI can be obtained by the proposed path selection mechanism compared with the typical shortest delay path (SDP) strategy, minimum spanning tree (MST) strategy, and MAoIG. In particular, the numerical findings show that the proposed LUR reduces average AoI by a maximum of 12.66% compared with SDP, 75.28% compared with MST, and 69.3% compared with MAoIG, respectively, under different scenarios.

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.

Minimal Spanning Tree application to determine market correlation structure

Determining the structure of market correlation is an important topic in theory and experiments. Under the impact of the Covid-19 pandemic, the market structure may be deformed. Therefore, this study examines the pandemic’s impact on the market structure. This study considered the correlation structure of the VN30 portfolio (including 30 stocks with the largest market capitalization); the collecting period is from July 28, 2000, to July 30, 2021. The data was divided into 02 phases before and after the pandemic. The Kruskal algorithm is implemented to determine the Minimal Spanning Tree (MST) structure to define the structure of market correlation. This study compared the change in the structure before and after the Covid-19 pandemic by structures’ mean of distances comparison. T-test results show that there are structural differences before and after the pandemic. Based on the research result, investors should change their risk management strategy to suit the market context because the previous structure has been changed.

Clustering in Oxygen Nuclei and Spectator Fragments in 16O–16O Collisions at the LHC

A new version of the Abrasion–Ablation Monte Carlo for Colliders model with the Minimum Spanning Tree clusterization algorithm (AAMCC-MST) is used to simulate 16O–16O collisions at the LHC, accounting for the presence of alpha-clustered states in 16O. The yields of He, Li, Be, B, C and N spectator nuclei are calculated taking into account the pre-equilibrium clusterization of spectator matter and short-range correlations (SRC) between nucleons in 16O. The impact of α-clustering and SRC on the production of spectator neutrons and deuterons is investigated. The results on the production of spectator nucleons and fragments can help in evaluating the performance of Zero Degree Calorimeters in future studies of 16O–16O collisions at the LHC.

Integrating Quantum Computing into De Novo Metabolite Identification

Tandem mass spectrometry (MS/MS) is a widely used technology for identifying metabolites. De novo metabolite identification is an identification strategy that does not refer to any spectral or metabolite database. However, this strategy is time-consuming and cannot meet the need for high-throughput metabolite identification. Böcker et al. converted the de novo identification problem into the maximum colorful subtree (MCS) problem. Unfortunately, the MCS problem is NPhard, which indicates there are no existing efficient exact algorithms. To address this issue, we propose to apply quantum computing to accelerate metabolite identification. Quantum computing performs computations on quantum computers. The recent progress in this area has brought the hope of making some computationally intractable areas trackable, although there are still no general approaches to converting regular computer algorithms into quantum algorithms. Specifically, there is no efficient quantum algorithm for the MCS problem. The MCS problem can be considered as the combination of many maximum spanning tree problems that can be converted into minimum spanning tree problems. This work applies a quantum algorithm designed for the minimum spanning problem to speed up de novo metabolite identification. The possible strategy for further improving the performance is also briefly discussed.

Portfolio Optimization Using Minimum Spanning Tree Model in the Moroccan Stock Exchange Market

Portfolio optimization is a pertinent topic of significant importance in the financial literature. During the portfolio construction, an investor confronts two important steps: portfolio selection and portfolio allocation. This article seeks to investigate portfolio optimization based on the Minimum Spanning Tree (MST) method applied on the Moroccan All Shares Index (MASI) historical stock log returns covering the period from 2 January 2013 to 27 October 2022 allowing us to build two portfolios: MST-Portfolio and MST-Portfolio 2. Portfolio selection was carried out for MST-Portfolio and MST-Portfolio 2, respectively, based on 63 stocks or using the Degree Centrality (DC) measure and portfolio allocation for both portfolios was carried through the use of the Inverse Degree Centrality Portfolio (IDCP). The obtained portfolios were compared with the Minimum Variance Portfolio (MV Portfolio) and Equal Weighting Portfolio (EW Portfolio) using centrality measures, diversification, and backtesting. According to the used indicators analysis, MST-Portfolio and MST-Portfolio 2 are the most well-performed and robust portfolios showing a good performance during the studied period, even during the COVID-19 crisis, and ensuring a good level of diversification. The findings demonstrate that both suggested methods can enhance portfolio performance, evidence that can help investors or active managers when optimizing their portfolios.

Risk spillover networks in financial markets: Evidence from emerging markets

AbstractThis paper empirically explores dynamic risk impact of extreme volatility between stock and foreign exchange markets in emerging markets. Based on CoVaR analysis, we construct networks to investigate the nonlinear and dynamic evolution characteristics of risk contagion. The results show that stock and foreign exchange markets exhibit asymmetric tail dependence. All networks present small world network characteristics. The risk tolerance impact is more noticeable than risk overflow and stock markets are more sensitive to risk contagion. In the minimum spanning tree (MST), Korean stock market and foreign exchange markets of India and China are critical nodes in the minimum path of risk overflow.

MCMSTClustering: defining non-spherical clusters by using minimum spanning tree over KD-tree-based micro-clusters

MCMSTClustering: defining non-spherical clusters by using minimum spanning tree over KD-tree-based micro-clusters

Reconstructing B cell lineage trees with minimum spanning tree and genotype abundances

B cell receptor (BCR) genes exposed to an antigen undergo somatic hypermutations and Darwinian antigen selection, generating a large BCR-antibody diversity. This process, known as B cell affinity maturation, increases antibody affinity, forming a specific B cell lineage that includes the unmutated ancestor and mutated variants. In a B cell lineage, cells with a higher antigen affinity will undergo clonal expansion, while those with a lower affinity will not proliferate and probably be eliminated. Therefore, cellular (genotype) abundance provides a valuable perspective on the ongoing evolutionary process. Phylogenetic tree inference is often used to reconstruct B cell lineage trees and represents the evolutionary dynamic of BCR affinity maturation. However, such methods should process B-cell population data derived from experimental sampling that might contain different cellular abundances. There are a few phylogenetic methods for tracing the evolutionary events occurring in B cell lineages; best-performing solutions are time-demanding and restricted to analysing a reduced number of sequences, while time-efficient methods do not consider cellular abundances. We propose ClonalTree, a low-complexity and accurate approach to construct B-cell lineage trees that incorporates genotype abundances into minimum spanning tree (MST) algorithms. Using both simulated and experimental data, we demonstrate that ClonalTree outperforms MST-based algorithms and achieves a comparable performance to a method that explores tree-generating space exhaustively. Furthermore, ClonalTree has a lower running time, being more convenient for building B-cell lineage trees from high-throughput BCR sequencing data, mainly in biomedical applications, where a lower computational time is appreciable. It is hundreds to thousands of times faster than exhaustive approaches, enabling the analysis of a large set of sequences within minutes or seconds and without loss of accuracy. The source code is freely available at github.com/julibinho/ClonalTree.

Lazy Parameter Tuning and Control: Choosing All Parameters Randomly from a Power-Law Distribution

Most evolutionary algorithms have multiple parameters and their values drastically affect the performance. Due to the often complicated interplay of the parameters, setting these values right for a particular problem (parameter tuning) is a challenging task. This task becomes even more complicated when the optimal parameter values change significantly during the run of the algorithm since then a dynamic parameter choice (parameter control) is necessary. In this work, we propose a lazy but effective solution, namely choosing all parameter values (where this makes sense) in each iteration randomly from a suitably scaled power-law distribution. To demonstrate the effectiveness of this approach, we perform runtime analyses of the (1+(λ,λ))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1+(\\lambda ,\\lambda ))$$\\end{document} genetic algorithm with all three parameters chosen in this manner. We show that this algorithm on the one hand can imitate simple hill-climbers like the (1+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1+1)$$\\end{document} EA, giving the same asymptotic runtime on problems like OneMax, LeadingOnes, or Minimum Spanning Tree. On the other hand, this algorithm is also very efficient on jump functions, where the best static parameters are very different from those necessary to optimize simple problems. We prove a performance guarantee that is comparable to the best performance known for static parameters. For the most interesting case that the jump size k is constant, we prove that our performance is asymptotically better than what can be obtained with any static parameter choice. We complement our theoretical results with a rigorous empirical study confirming what the asymptotic runtime results suggest.

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.

A hybrid technique using minimal spanning tree and analytic hierarchical process to prioritize functional requirements for parallel software development

A hybrid technique using minimal spanning tree and analytic hierarchical process to prioritize functional requirements for parallel software development

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.

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.

Minimum spanning tree dynamic programming stereo‐matching method based on superpixels

AbstractThe minimum spanning tree (MST) stereo‐matching method is an information‐infiltration process. The difference in edge attributes of an MST can cause the edge‐expansion phenomenon, which affects the matching accuracy. To accurately recover image‐depth information, a dynamic‐programming stereo‐matching method based on the MST was proposed. First, the colour Birchfield Tomasi cost‐calculation method based on image adaptive colour information was proposed to obtain stable initial cost values. Second, the image was segmented into superpixel regions using the simple linear iterative clustering algorithm. The pixel‐ and region‐level MSTs were then constructed. Next, combined with the idea of dynamic programming, the MST cost‐aggregation process was re‐deduced. On this basis, the aggregate cost values of the two MSTs were obtained. Finally, the aggregate cost values were combined adaptively to acquire the high‐precision smooth disparity map. The Middlebury 2014 dataset was used for the experiments. The experimental results indicate that the proposed method can effectively improve the accuracy of stereo‐matching.

Effective enhancement of isolation Forest method based on Minimal Spanning tree clustering

Modern technologies let researchers and practitioners explore large datasets. Anomaly detection methods applied to fix or delete unwanted records are of great importance here. One of the fastest and the most effective algorithms of anomaly detection is Isolation Forest. This solution is based on building isolation binary trees by randomly splitting the dataset elements. In this manuscript, we propose an innovative approach modifying this technique. In particular, we replace random divisions in the base mechanism with divisions based on Minimal Spanning Tree clustering. Additionally, we improve the evaluation process by introducing a two-component score function. The first component is related to the level of the test element in the isolation tree. The second term is calculated as the distance between specific points in the last split node. Namely, between the value of the evaluated attribute and the partition center stored in the node. In a series of comprehensive experiments, the proposed approach was compared with other Isolation Forest-based algorithms as well as state-of-the-art competing solutions. Our enhancement has proved its advantage in classification quality. In addition, the implementation operation times of selected solutions were measured. The results clearly demonstrate high effectiveness of the proposed approach.

Study on Chains of Information Industry based on Average Propagation Lengths and Minimal Spanning Tree

Compared with the traditional methods of using industrial linkages to analyze the industrial chain, this paper introduces the theories of economic distance and graph theory to analyze the information industry chain. Industrial linkages reflects the size of economic and technological connection, and economic distance measures the distance between industries. The minimum spanning tree in graph theory measures the position of each industry in the information industry chain. There are complex indirect dependence and direct dependence in the industrial chain of electronic product manufacturing. The economic distance with most industries is 2 and 3, and most of the associated industries are manufacturing. The industrial chain of information service industry is relatively simple. Most related industries belong to the tertiary industry, and the economic distance is relatively close. The minimum spanning tree of information industry shows the central position of metal ore and metal smelting, and shows that the information industry chain still depends on metal ore resources. Using the time series input-output table, this paper analyzes the development and changes of the information industry chain, and finds that the information industry chain is relatively stable in this time span. Finally, it compares the difference between the competitive model and the non competitive model to measure the information industry chain. Using the non competitive model, it is found that the information industry chain becomes shorter and the economic distance between industries is closer.

Reconstruction of Single-Cell Trajectories Using Stochastic Tree Search.

The recent advancement in single-cell RNA sequencing technologies enables the understanding of dynamic cellular processes at the single-cell level. Using trajectory inference methods, pseudotimes can be estimated based on reconstructed single-cell trajectories which can be further used to gain biological knowledge. Existing methods for modeling cell trajectories, such as minimal spanning tree or k-nearest neighbor graph, often lead to locally optimal solutions. In this paper, we propose a penalized likelihood-based framework and introduce a stochastic tree search (STS) algorithm aiming at the global solution in a large and non-convex tree space. Both simulated and real data experiments show that our approach is more accurate and robust than other existing methods in terms of cell ordering and pseudotime estimation.

An oracle-based framework for robust combinatorial optimization

We propose a general solution approach for min-max-robust counterparts of combinatorial optimization problems with uncertain linear objectives. We focus on the discrete scenario case, but our approach can be extended to other types of uncertainty sets such as polytopes or ellipsoids. Concerning the underlying certain problem, the algorithm is entirely oracle-based, i.e., our approach only requires a (primal) algorithm for solving the certain problem. It is thus particularly useful in case the certain problem is well-studied but its combinatorial structure cannot be directly exploited in a tailored robust optimization approach, or in situations where the underlying problem is only defined implicitly by a given software. The idea of our algorithm is to solve the convex relaxation of the robust problem by a simplicial decomposition approach, the main challenge being the non-differentiability of the objective function in the case of discrete or polytopal uncertainty. The resulting dual bounds are then used within a tailored branch-and-bound framework for solving the robust problem to optimality. By a computational evaluation, we show that our method outperforms straightforward linearization approaches on the robust minimum spanning tree problem. Moreover, using the Concorde solver for the certain oracle, our approach computes much better dual bounds for the robust traveling salesman problem in the same amount of time.