The Maximum and Minimum Value of Exponential RandićIndices of Quasi-Tree Graph

The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.

Graph Convolutional Networks Embedding Textual Structure Information for Relation Extraction

Deep neural network-based relational extraction research has made significant progress in recent years,andit provides data support for many natural language processing downstream tasks such as building knowledgegraph,sentiment analysis and question-answering systems.However,previous studies ignored much unusedstructural information in sentences that could enhance the performance of the relation extraction task.Moreover,most existing dependency-based models utilize self-attention to distinguish the importance of context,whichhardly deals withmultiple-structure information.To efficiently leverage multiple structure information,this paperproposes a dynamic structure attention mechanism model based on textual structure information,which deeplyintegrates word embedding,named entity recognition labels,part of speech,dependency tree and dependency typeinto a graph convolutional network.Specifically,our model extracts text features of different structures from theinput sentence.Textual Structure information Graph Convolutional Networks employs the dynamic structureattention mechanism to learn multi-structure attention,effectively distinguishing important contextual features invarious structural information.In addition,multi-structure weights are carefully designed as amergingmechanismin the different structure attention to dynamically adjust the final attention.This paper combines these featuresand trains a graph convolutional network for relation extraction.We experiment on supervised relation extractiondatasets including SemEval 2010 Task 8,TACRED,TACREV,and Re-TACED,the result significantly outperformsthe previous.

An effective multi-level algorithm based on ant colony optimization for graph bipartitioning

Partitioning is a fundamental problem with applications to many areas including data mining, parellel processing and Very-large-scale integration （VLSI） design. An effective multi-level algorithm for bisecting graph is proposed. During its coarsening phase, an improved matching approach based on the global information of the graph core is developed with its guidance function. During the refinement phase, the vertex gain is exploited as ant＇s heuristic information and a positive feedback method based on pheromone trails is used to find the global approximate bipartitioning. It is implemented with American National Standards Institute （ANSI） C and compared to MeTiS. The experimental evaluation shows that it performs well and produces encouraging solutions on 18 different graphs benchmarks.

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.

Minimum Dominating Tree Problem for Graphs

A dominating tree T of a graph G is a subtree of G which contains at least one neighbor of each vertex of G.The minimum dominating tree problem is to find a dominating tree of G with minimum number of vertices,which is an NP-hard problem.This paper studies some polynomially solvable cases,including interval graphs,Halin graphs,special outer-planar graphs and others.

On the ordering of the Kirchhoff indices of the complements of trees and unicyclic graphs

The Kirchhoff index Kf(G) of a graph G is defined to be the sum of the resistance distances between all pairs of vertices of G. In this paper, we develop a novel method for ordering the Kirchhoff indices of the complements of trees and unicyclic graphs. With this method, we determine the first five maximum values of Kf■ and the first four maximum values of Kf(ū),where ■ and ū are the complements of a tree T and unicyclic graph U, respectively.

The Dynamic-to-Static Conversion of Dynamic Fault Trees Using Stochastic Dependency Graphs and Stochastic Activity Networks

In this paper a new modeling framework for the dependability analysis of complex systems is presented and related to dynamic fault trees (DFTs). The methodology is based on a modular approach: two separate models are used to handle, the fault logic and the stochastic dependencies of the system. Thus, the fault schema, free of any dependency logic, can be easily evaluated, while the dependency schema allows the modeler to design new kind of non-trivial dependencies not easily caught by the traditional holistic methodologies. Moreover, the use of a dependency schema allows building a pure behavioral model that can be used for various kinds of dependability studies. In the paper is shown how to build and integrate the two modular models and convert them in a Stochastic Activity Network. Furthermore, based on the construction of the schema that embeds the stochastic dependencies, the procedure to convert DFTs into static fault trees is shown, allowing the resolution of DFTs in a very efficient way.

Uniquely Tree Colorable Graphs

In this paper, the concepts of tree chromatic numbers and uniquely tree colorable graphs are introduced. After discussion some fundamental properties, three necessary conditions for a simple graph to be uniquely tree colorable are given. Moreover, a series of uniquely tree colorable graphs are constructed.

Individual tree extraction from terrestrial laser scanning data via graph pathing

Background:Individual tree extraction from terrestrial laser scanning(TLS)data is a prerequisite for tree-scale estimations of forest biophysical properties.This task currently is undertaken through laborious and time-consuming manual assistance and quality control.This study presents a new fully automatic approach to extract single trees from large-area TLS data.This data-driven method operates exclusively on a point cloud graph by path finding,which makes our method computationally efficient and universally applicable to data from various forest types.Results:We demonstrated the proposed method on two openly available datasets.First,we achieved state-of-the-art performance on locating single trees on a benchmark dataset by significantly improving the mean accuracy by over 10% especially for difficult forest plots.Second,we successfully extracted 270 trees from one hectare temperate forest.Quantitative validation resulted in a mean Intersection over Union(mIoU)of 0.82 for single crown segmentation,which further led to a relative root mean square error(RMSE%)of 21.2% and 23.5% for crown area and tree volume estimations,respectively.Conclusions:Our method allows automated access to individual tree level information from TLS point clouds.The proposed method is free from restricted assumptions of forest types.It is also computationally efficient with an average processing time of several seconds for one million points.It is expected and hoped that our method would contribute to TLS-enabled wide-area forest qualifications,ranging from stand volume and carbon stocks modelling to derivation of tree functional traits as part of the global ecosystem understanding.

An Optimal Parallel Algorithm for Constructing a Spanning Tree on Proper Circle Trapezoid Graphs

Given a simple graph G with n vertices and m edges, the spanning tree problem is to find a spanning tree for a given graph G. This problem has many applications, such as electric power systems, computer network design and circuit analysis. For a simple graph, the spanning tree problem can be solved in O(log n) time with O(m+n) processors on the CRCW PRAM. In general, it is known that more efficient parallel algorithms can be developed by restricting classes of graphs. In this paper, we shall propose a parallel algorithm which runs O(log n) time with O(n/log n) processors on the EREW PRAM for constructing on proper circle trapezoid graphs.

The Rupture Degree of Graphs with k-Tree

A k-tree of a connected graph G is a spanning tree with maximum degree at most k. The rupture degree for a connected graph G is defined by , where and , respectively, denote the order of the largest component and number of components in . In this paper, we show that for a connected graph G, if for any cut-set , then G has a k-tree.

Clique-transversal number of graphs whose clique-graphs are trees

Given a graph G, a subgraph C is called a clique of G if C is a complete subgraph of G maximal under inclusion and ｜C｜ ≥2. A clique-transversal set S of G is a set of vertices of G such that S meets all cliques of G. The clique-transversal number, denoted as τC（G）, is the minimum cardinality of a clique-transversal set in G. The clique-graph of G, denoted as K（G）, is the graph obtained by taking the cliques of G as vertices, and two vertices are adjacent if and only if the corresponding cliques in G have nonempty intersection. Let F be a class of graphs G such that F = {G｜ K（G） is a tree}. In this paper the graphs in F having independent clique-transversal sets are shown and thus τC（G）/｜G｜ ≤ 1/2 for all G ∈F.

The Number of Maximal Independent Sets in Quasi-Tree Graphs and Quasi-Forest Graphs

A maximal independent set is an independent set that is not a proper subset of any other independent set. A connected graph (respectively, graph) G with vertex set V(G) is called a quasi-tree graph (respectively, quasi-forest graph), if there exists a vertex x ∈V(G) such that G −x?is a tree (respectively, forest). In this paper, we survey on the large numbers of maximal independent sets among all trees, forests, quasi-trees and quasi-forests. In addition, we further look into the problem of determining the third largest number of maximal independent sets among all quasi-trees and quasi-forests. Extremal graphs achieving these values are also given.

Graph Similarity Join with K-Hop Tree Indexing

Graph similarity join has become imperative for integrating noisy and inconsistent data from multiple data sources. The edit distance is commonly used to measure the similarity between graphs. To accelerate the similarity join based on graph edit distance, in the paper, we make use of a preprocessing strategy to remove the mismatching graph pairs with significant differences. Then a novel method of building indexes for each graph is proposed by grouping the nodes which can be reached in k hops for each key node with structure conservation, which is the k-hop-tree based indexing method. Experiments on real and synthetic graph databases also confirm that our method can achieve good join quality in graph similarity join. Besides, the join process can be finished in polynomial time.

融合词法句法信息的方面级情感分析模型

为解决现有方面级情感分析方法缺乏句法约束和词义信息的问题,将句法依存树和知识图谱融合起来对句子编码,提出一种词法句法相结合的图神经网络模型。利用图神经网络分别提取句法依存树中的句法信息和知识图谱中的词法信息,经过位置编码模块和掩码加权模块捕捉重要性更高的单词;将两种特征进行结合获得融合句法词法信息的文本表示,进行情感分类。在3个公开数据集上的实验结果验证了该模型的有效性。

无爪图的支撑k-端点树的存在性

树T中度为1的点称为叶子,叶子数目不超过k的树称为k-端点树.图中存在一个哈密尔顿路,说明图中存在恰好含有两个叶子的支撑树.自然就有了关于哈密尔顿路问题的一个推广:考虑图中至多有k个叶子的支撑树即支撑k-端点树的存在性问题.通过控制集参数,确定了连通无爪图中存在支撑k-端点树条件.

字典积图的任意可分性

给定n个顶点的图G,对于满足∑_(i=1)^(k)n_(i)=n的任意一个正整数序列(n_(1),n_(2),…,n_(k)),如果都存在顶点集V(G)的划分(V_(1),V_(2),…,V_(k)),满足Vi导出的子图G[V_(i)]是连通的,并且|V_(i)|=n_(i),其中1≤i≤k,则称图G是任意可分图(简称为AP).两个图G和H的字典积图记为G?H,其顶点集为V(G)×V(H),(g,h)(g,h)是G?H的一条边当且仅当gg∈E(G)或者g=g且hh∈E(H).讨论了可迹图和任意可分图的字典积图的任意可分性,证明了对于最大度至多为n+1的树T,如果T有一条路P满足全部度数为(T)的顶点属于顶点集V(P),则字典积图T○Pn是任意可分图;如果G是一个可迹图且H是任意可分图,则图G○H是任意可分图;如果G=S(2,a,b)是一个满足2≤a≤b的任意可分星型树,则图G○G是任意可分图;如果G是哈密顿图且H是一个图,则G○H是任意可分图.

基于异构环境的Out-Tree任务图的调度算法

分布式应用程序的有效调度是异构计算系统中的一个关键问题。目前已有的Out-Tree任务图的调度算法大多基于同构环境而开发,未考虑处理机的异构性,导致调度的效率较低。针对异构计算环境,提出一个基于列表和任务复制的Out-Tree任务图的静态启发式贪心调度算法,其时间复杂度为O(hv2 p),其中h、v和p分别表示任务图的高度、任务个数和调度使用的处理机个数。实验结果表明,相比其他算法,该算法能提供调度长度较短、处理机使用较少的有效调度,其应用性更强。

基于依赖增强的分层抽象语法树的代码克隆检测

在软件工程领域,基于语义相似的代码克隆检测方法可以降低软件维护的成本并预防系统漏洞,抽象语法树(AST)作为典型的代码抽象表征形式,已成功应用于多种程序语言的代码克隆检测任务,然而现有工作主要利用原始AST提取代码的语义,没有深入挖掘AST中的深层语义和结构信息。针对上述问题,提出一种基于依赖增强的分层抽象语法树(DEHAST)的代码克隆检测方法。首先,对AST进行分层处理,将AST划分得到不同的语义层次;其次,为AST的不同层次添加相应的依赖增强边构建DEHAST,将简单的AST变成具有更丰富程序语义的异构图;最后,使用图匹配网络(GMN)模型检测异构图的相似性,实现代码克隆检测。在BigCloneBench和Google Code Jam两个数据集上的实验结果显示,DEHAST能够检测100%的Type-1和Type-2代码克隆、99%的Type-3代码克隆和97%的Type-4代码克隆;与基于树的方法ASTNN(AST-based Neural Network)相比,F1分数均提高了4个百分点,验证了DEHAST可以较好地完成代码语义克隆检测。

Packing 4-Partite Tree into Complete 4-Partite Graph

For graphs G and H,an embedding of G into H is an injection ϕ:V(G)→V(H)such that ϕ(a)ϕ(b)∈E(H)whenever ab∈E(G).A packing of p graphs G_(1),G_(2),…,G_(p) into H is a p-tupleΦ=(ϕ_(1),ϕ_(2),…,ϕ_(p))such that,for i=1,2,…,p,ϕ_(i) is an embedding of Gi into H and the p sets ϕ_(i)(E(G_(i)))are mutually disjoint.Motivated by the"Tree Packing Conjecture"made by Gyar fas and Lehel,Wang Hong conjectured that for each k-partite tree,there is a packing of two copies of T(X)into a complete k-partite graph B_(n+m)(Y),where m=■k/2」..In this paper,we confirm this conjecture for k=4.