On Spanning Wide Diameter of Graphs

A t-container Ct(u,v)is a set of t internally disjoint paths between two distinct vertices u and v in a graph G,i.e.,Ct(u,v)={P_(1),P_(2),···,Pt}.Moreover,if V(P_(1))∪V(P_(2))∪···∪V(Pt)=V(G)then Ct(u,v)is called a spanning t-container,denoted by C_(t)^(sc)(u,v).The length of C_(t)^(sc)(u,v)={P_(1),P_(2),···,Pt}is l(C_(t)^(sc)(u,v))=max{l(P_(i))|1≤i≤t}.A graph G is spanning t-connected if there exists a spanning t-container between any two distinct vertices u and v in G.Assume that u and v are two distinct vertices in a spanning t-connected graph G.Let D_(t)^(sc)(u,v)be the collection of all C_(t)^(sc)(u,v)’s.Define the spanning t-wide distance between u and v in G,d_(t)^(sc)(u,v)=min{l(C_(t)^(sc)(u,v))|C_(t)^(sc)(u,v)∈D_(t)^(sc)(u,v)},and the spanning t-wide diameter of G,D_(t)^(sc)(G)=max{d_(t)^(sc)(u,v)|u,v∈V(G)}.In particular,the spanning wide diameter of G is D_(κ)^(sc)(G),whereκis the connectivity of G.In the paper we provide the upper and lower bounds of the spanning wide diameter of a graph,and show that the bounds are best possible.We also determine the exact values of wide diameters of some well known graphs including Harary graphs and generalized Petersen graphs et al..

The effect of functional loads on free spanning pipeline's VIV response

During the operation and installation of offshore pipelines, high axial forces and pressures are experienced, and their effects cannot be neglected. In this article, the effect of internal flow velocity and functional loads on vortex-induced vibration （VIV） response is investigated. On the basis of the Hamilton principle, a differential equation was derived to describe the motion of a pinned-pinned tensioned spanning pipeline conveying fluid. The VIV response was calculated according to DNV-RP-F105 under different functional loads. The results showed that functional loads influence free spanning pipeline VIV response by changing the natural frequency. Internal flow velocity was found less important for VIV response than other functional load factors, such as effective axial force, because the speed in reality is not high enough to be significant. The research may provide a reference for sensitivity studies of the effect of functional loads on allowable free span lengths.

An Explicit Integer Programming Model of the Minimal Spanning Tree Problem for Digraphs with Asymmetric Weights

As far as the minimal spanning tree problem for the digraph with asymmetric weightsis concerned, an explicit integer programming model is proposed, which could be solved successfullyusing the integer programming packages such as LINDO, and furthermore this model is extendedinto the stochastic version, that is, the minimal spanning tree problem for the digraph with theweights is not constant but random variables. Several algorithms are also developed to solve themodels. Finally, a numerical demonstration is given.

基于最小Spanning树的中继节点部署算法

在能量受限的无线传感器网络(WSNs)中,部署中继节点成为确保通信覆盖的常用方法。提出基于最小Spanning树的中继节点部署算法(MST-DRN)。MST-DRN算法引用基于无线充电的能量模型。再依据节点的能量采集率计算边权值。依据边权值的图模型构建最小Spanning树(MST)。检测MST中不满足生存条件的非支叶节点,在节点附近部署中继节点,维持网络连通。实验数据表明:提出的MST-DRN算法在确保网络连通时,减少了成本(中继节点数),并提高了数据包传递率。

A NEW ALGORITHM FOR ALL EFFICIENT SPANNING TREES

In Corley′s algorithm for all efficient spanning trees, final solutions include many spanning trees, which are not all efficient. In this paper, a new algorithm is presented, which corrects and modifies Corley′s algorithm. A necessary condition is developed for the subtree of an efficient spanning tree. According to the condition the new algorithm is established and its efficiency is proved.

Experimental Study on Free Spanning Submarine Pipeline Under Dynamic Excitation

Seismic load has a significant effect on the response of a free spanning submarine pipeline when the pipeline is constructed in a seismically active region. The model experiment is performed on an underwater shaking table to simulate the response of submarine pipelines under dynamic input. In consideration of the effects of the terrestrial and submarine pipeline, water depth, support condition, distance from seabed, empty and full pipeline, and span on dynamic response, 120 groups of experiments are conducted. Affecting factors are analyzed and conclusions are drawn for reference. For the control of dynamic response, the span of a submarine pipeline is by far more important than the other factors. Meanwhile, the rosponse difference between a submarine pipeline under sine excitation and that under random excitation exists in experiments.

Analysis of Dynamic Characteristics of Submarine Free Spanning Pipelines by Complex Damping Method

Considering the effect of the internal flowing fluid and the external marine environmental condition, the differential equation for the vortex induced vibration (VIV) of the free spanning pipeline is derived and is discretized by the Hermit interpolation function. The free vibration equation with the damping term is solved by the complex damping method for the natural frequency, and then the effect of fluid damping on the natural frequency of the free spanning pipeline is analyzed. The results show that fluid damping has a significant influence on the damped natural frequency of the free spanning pipeline in the lock in state, while it has little influence when the pipeline is out of the lock in state. In the meantime, the change of the free span length has the same effect on the damped natural frequency and the undamped natural frequency.

Study on Model Tests and Hydrodynamic Force Models for Free Spanning Submarine Pipelines Subjected to Earthquakes

A test rig is built to model the dynamic response of submarine pipelines with an underwater shaking table in the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, China. Model tests are carried out to consider the effects of exciting wave directions and types. Based on the experimental results, two hydrodynamic force models derived from Morisen equation and Wake model are presented respectively. By use of hydrodynamic force models suitable for free spanning submarine pipelines under earthquakes, diseretized equations of motion are obtained and finite element models are established to analyze dynamic response of free spanning submarine pipeline subjected to multi-support seismic excitations. The comparison of numerical results with experimental results shows that the improved Morison and Wake hydrodynamic force models could satisfactorily predict dynamic response on the free spanning submarine pipelines subjected to earthquakes.

SOLVING MINIMUM SPANNING TREE PROBLEM WITH DNA COMPUTING

Molecular programming is applied to minimum spanning problem whose solution requires encoding of real values in DNA strands. A new encoding scheme is proposed for real values that is biologically plausible and has a fixed code length. According to the characteristics of the problem, a DNA algorithm solving the minimum spanning tree problem is given. The effectiveness of the proposed method is verified by simulation. The advantages and disadvantages of this algorithm are discussed.

Spanning tree-based algorithm for hydraulic simulation of large-scale water supply networks

With the purpose of making calculation more efficient in practical hydraulic simulations, an improved algorithm was proposed and was applied in the practical water distribution field. This methodology was developed by expanding the traditional loop-equation theory through utilization of the advantages of the graph theory in efficiency. The utilization of the spanning tree technique from graph theory makes the proposed algorithm efficient in calculation and simple to use for computer coding. The algorithms for topological generation and practical implementations are presented in detail in this paper. Through the application to a practical urban system, the consumption of the CPU time and computation memory were decreased while the accuracy was greatly enhanced compared with the present existing methods.

A Table Based Algorithm for MinimumDirected Spanning Trees

As far as the weighted digraph is considered, an optimal directed spanning tree algorithm called table based algorithm (TBA) is proposed in the paper based on the table instead of the weighted digraph. The optimality is proved, and a numerical example is demonstrated.

Table Operation Method for Optimal Spanning Tree Problem

As far as the weight digraph is considered, based on the table instead of the weightdigraph, an optimal spanning tree method called the Table Operations Method (TOM) is proposed.And the optimality is proved and a numerical example is demonstrated.

MINIMUM CONGESTION SPANNING TREES IN BIPARTITE AND RANDOM GRAPHS

The first problem considered in this article reads： is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs？ It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n3/2, where n is the number of vertices. The second problem is to estimate spanning tree congestion of random graphs. It is proved that the standard model of random graphs cannot be used to find graphs whose spanning tree congestion has order greater than n3/2.

The minimal spanning tree method for calculating seismic multi-fractal

There are many methods to calculate seismic fractal at present. However, there are still more or less questions to every method. In this paper, we introduce a new way to calculate seismic fractal-the minimal spanning tree. We make an important improvement for this method. By studying some seismic events of four regions including Wushi, Wusu, Tangshan and Haicheng, we obtain that before the strong earthquake occurrence, the multi-fractal spectrum of the space-time distribution of earthquakes changes from centralized to loose. The result shows that the complexity of fractal structure and the inhomogeneity of the space-time distribution of earthquakes are both increasing. By studying the numerical simulation of point sets, we draw the conclusion that the physical essence of multi-fractal spectrums before and after a strong earthquake occurrence is a changing process from homogeneous to inhomogeneous, from simple to complex.

Brain Functional Network Based on Small-Worldness and Minimum Spanning Tree for Depression Analysis

Since the outbreak and spread of corona virus disease 2019(COVID-19),the prevalence of mental disorders,such as depression,has continued to increase.To explore the abnormal changes of brain functional connections in patients with depression,this paper proposes a depression analysis method based on brain function network(BFN).To avoid the volume conductor effect,BFN was constructed based on phase lag index(PLI).Then the indicators closely related to depression were selected from weighted BFN based on small-worldness(SW)characteristics and binarization BFN based on the minimum spanning tree(MST).Differences analysis between groups and correlation analysis between these indicators and diagnostic indicators were performed in turn.The resting state electroencephalogram(EEG)data of 24 patients with depression and 29 healthy controls(HC)was used to verify our proposed method.The results showed that compared with HC,the information processing of BFN in patients with depression decreased,and BFN showed a trend of randomization.

Study on Pure IL VIV of A Free Spanning Pipeline Under General Boundary Conditions

Pipeline spans may occur due to natural seabed irregularities or local scour of bed sediment. The pure in-line（IL）vortex-induced vibrations（VIV） analysis of the free spans is an important subject for design of pipeline in uneven seabed. The main objective of this paper is to analyze the characteristics of pure IL VIV of a free spanning pipeline under general boundary conditions. An IL wake oscillator model which can describe the coupling of pipeline structure and fluctuating drag is introduced and employed. The coupled partial differential equations of structure and wake are transformed into a set of ordinary differential equations using two-mode Galerkin method. Some case studies are presented and thoroughly discussed in order to investigate the effects of internal fluid, axial force and boundary conditions on the pure IL VIV.

High-resolution Remote Sensing Image Segmentation Using Minimum Spanning Tree Tessellation and RHMRF-FCM Algorithm

It is proposed a high resolution remote sensing image segmentation method which combines static minimum spanning tree(MST)tessellation considering shape information and the RHMRF-FCM algorithm.It solves the problems in the traditional pixel-based HMRF-FCM algorithm in which poor noise resistance and low precision segmentation in a complex boundary exist.By using the MST model and shape information,the object boundary and geometrical noise can be expressed and reduced respectively.Firstly,the static MST tessellation is employed for dividing the image domain into some sub-regions corresponding to the components of homogeneous regions needed to be segmented.Secondly,based on the tessellation results,the RHMRF model is built,and regulation terms considering the KL information and the information entropy are introduced into the FCM objective function.Finally,the partial differential method and Lagrange function are employed to calculate the parameters of the fuzzy objective function for obtaining the global optimal segmentation results.To verify the robustness and effectiveness of the proposed algorithm,the experiments are carried out with WorldView-3(WV-3)high resolution image.The results from proposed method with different parameters and comparing methods(multi-resolution method and watershed segmentation method in eCognition software)are analyzed qualitatively and quantitatively.

AEESPAN: Automata Based Energy Efficient Spanning Tree for Data Aggregation in Wireless Sensor Networks

In Wireless Sensor Networks (WSNs), sensor nodes are developed densely. They have limit processing ca-pability and low power resources. Thus, energy is one of most important constraints in these networks. In some applications of sensor networks, sensor nodes sense data from the environment periodically and trans-mit these data to sink node. In order to decrease energy consumption and so, increase network’s lifetime, volume of transmitted data should be decreased. A solution, which is suggested, is aggregation. In aggrega-tion mechanisms, the nodes aggregate received data and send aggregated result instead of raw data to sink, so, the volume of the transmitted data is decreased. Aggregation algorithms should construct aggregation tree and transmit data to sink based on this tree. In this paper, we propose an automaton based algorithm to con-struct aggregation tree by using energy and distance parameters. Automaton is a decision-making machine that is able-to-learn. Since network’s topology is dynamic, algorithm should construct aggregation tree peri-odically. In order to aware nodes of topology and so, select optimal path, routing packets must be flooded in entire network that led to high energy consumption. By using automaton machine which is in interaction with environment, we solve this problem based on automat learning. By using this strategy, aggregation tree is reconstructed locally, that result in decreasing energy consumption. Simulation results show that the pro-posed algorithm has better performance in terms of energy efficiency which increase the network lifetime and support better coverage.

THE DESIGN AND ANALYSIS OF ALGORITHM OF MINIMUM COST SPANNING TREE

This paper provides a method of producing a minimum cost spanning tree (MCST) using set operations. It studies the data structure for implementation of set operations and the algorithm to be applied to this structure and proves the correctness and the complexity of the algorithm. This algorithm uses the FDG (formula to divide elements into groups) to sort (the FDG sorts a sequence of n elements in expected tir O(n)) and uses the method of path compression to find and to unite. Therefore. n produces an MCST of an undirected network having n vertices and e edges in expected time O(eG(n)).

A Novel Binary Firefly Algorithm for the Minimum Labeling Spanning Tree Problem

Given a connected undirected graph G whose edges are labeled,the minimumlabeling spanning tree(MLST)problemis to find a spanning tree of G with the smallest number of different labels.TheMLST is anNP-hard combinatorial optimization problem,which is widely applied in communication networks,multimodal transportation networks,and data compression.Some approximation algorithms and heuristics algorithms have been proposed for the problem.Firefly algorithm is a new meta-heuristic algorithm.Because of its simplicity and easy implementation,it has been successfully applied in various fields.However,the basic firefly algorithm is not suitable for discrete problems.To this end,a novel discrete firefly algorithm for the MLST problem is proposed in this paper.A binary operation method to update firefly positions and a local feasible handling method are introduced,which correct unfeasible solutions,eliminate redundant labels,and make the algorithm more suitable for discrete problems.Computational results show that the algorithm has good performance.The algorithm can be extended to solve other discrete optimization problems.