传输子网选择:度数有界最大支撑子图逼近

研究了源于无线网状网络的度数有界最大支撑子图问题:给定连通图G=(V,E)和正整数d≥2,求G的一个最大支撑子图H,满足对V中每个顶点v,v在H中的度数dH(v)不超过d。这里,支撑子图指图G的一个连通而且包括G中所有顶点的子图。就输入图的边是否带权,分别设计了多项式时间近似算法。当输入图为无权图时,证明了近似算法的近似比为2;当输入图为赋权图时,证明了算法输出一个最大度数不超过d+1、权重不低于最优解权重1/(d+2)的支撑子图。算法输出的度数有界支撑子图可以用作无线网状网络的传输子网。     

2r-正则图连通圈网络的Hamilton分解

互连网络是超级计算机的重要组成部分。互连网络通常模型化为一个图,图的顶点代表处理机,图的边代表通信链路。2010年师海忠提出互连网络的正则图连通圈网络模型,设计出了多种互连网络,也提出了一系列猜想。文中证明了2r -正则图连通圈网络可分解为边不交的一个Hamilton圈和一个完美对集的并,从而证明了当原图为2r-正则连通图时,这一系列猜想成立。     

递归型数据中心网络上g-额外连通度及容错单播算法研究

数据中心网络的研究是近几年兴起的热点。与传统的树型数据中心网络相比,递归型数据中心网络具有更好的容错性和可扩展性。部署于n-口交换机上的k-维递归型完全图网络可以表示为X_k,n,σ表示图中任意顶点与同维度其他子图相连接的边数。在实际情况中,网络的额外连通度相较于传统的连通度能够更准确地衡量一个网络的容错性。证明当k≥3,n≥3,σ∈{1,n-1}且0≤g≤2时,X_k,n的g-额外连通度为(g+1)(kσ-1)+n,这一结果接近于其连通度的g+1倍。进一步,提出基于该情形下的容错单播算法,并证明了该算法的时间复杂度和在最坏情况下X_k,n中任意两点间构造出路径长度的上界。通过模拟仿真实验,验证了该算法在执行效率上优于广度优先和深度优先搜索算法,且算法具有较好的容错性。     

基于分辨函数的极大团搜索算法

寻找极大团是几何图论极为重要的基础研究问题之一。将分辨函数模型与极大团性质结合,定义了顶点的极大团分辨函数、顶点关于某顶点子集的布尔映射函数,得到了一些与极大团相关的重要性质与定理,证明了图的极大团搜索问题可快捷自然地转换为相对简单的分辨函数表达式约束,为设计极大团搜索算法提供了一种有效的理论依据与求解途径。进而引入约简树构造方法设计了基于分辨函数的极大团搜索算法,最后通过给定无向连通图实例说明了算法的可行性与有效性。     

一种类间测试顺序改进算法

确定类的测试顺序是面向对象程序测试中的关键步骤。描述对象关系图模型,提出一种基于对象关系图的类间集成测试顺序改进算法,与Tai和Traon等人提出的算法相比,该算法需要的测试桩较少、效率较高。在Redflag4系统下用Kylix3(C++)对算法进行实现。理论分析和初步实验证明了该算法的可行性和有效性。     

基于扩展ORD图的类间集成测试顺序改进算法

在UML类图的基础上,将传统对象关系图(ORD)模型进行了扩展,并对它们进行了形式化的定义.提出了一种基于扩展ORD图的类间集成测试顺序改进算法,通过递归调用改进的Kosaraj鉴别强连通分量的算法来确定SCCs.本算法与Tai和Traon的两种算法比较,需要的测试桩最少,效率最高.理论分析和初步的实验证明这种方法是可行和有效的.     

测试算法评估及可测性预报系统

测试算法评估及可测性预报系统使用回归分析和遗传算法,为测试生成算法建立可测性参数的预报模型,使得对于给定电路,不必实际运行各测试生成算法,就可以快速评估并预报出最适合的算法。本文整体介绍了这一系统,并对其中各主要模块作了重点描述。     

基于回归分析的宏模型参数确定方法研究

为了解决装备测试性分析中宏模型参数确定问题,提出了一种新的求解方法。该算法基于回归分析原理,利用回归预测方程,有效地解决了宏模型参数确定问题,提高了测试性模型故障模式分析数据的可靠性,保证了测试性设计分析的顺利开展。经实例验证,此方法实现了给定条件下宏模型输入输出参数的确定,且运算复杂度低,参数确定过程耗时少,能够应用于复杂系统测试性设计分析与评估,已经在某装备测试性辅助设计与分析系统中得到应用。     

多智能体系统的最优持久编队生成策略

针对二维空间中减少智能体间通信链路的能量消耗问题,提出了一种基于最优刚性编队的最优持久编队生成算法.算法提出了针对智能体连通度数目的有向化操作方法,通过层层缩减最小刚性图范围的方式生成最优持久图,这种方法能对任意最小刚性图进行持久化,从理论上证明了算法的可操作性.仿真结果验证了算法的有效性.     

测试生成算法评估与预报系统

测试生成算法评估与预报系统分别利用回归算法、神经网络算法和遗传算法为测试生成算法建立预报模型,使得对给定电路,不必实际运行测试生成算法,就可快速地得到最有效的测试生成算法。对如何利用遗传算法建立预报模型进行了较为详细的论述。     

Property Testing in Bounded Degree Graphs

We further develop the study of testing graph properties as initiated by Goldreich, Goldwasser and Ron. Loosely speaking, given an oracle access to a graph, we wish to distinguish the case when the graph has a pre-determined property from the case when it is ``far'' from having this property. Whereas they view graphs as represented by their adjacency matrix and measure the distance between graphs as a fraction of all possible vertex pairs, we view graphs as represented by bounded-length incidence lists and measure the distance between graphs as a fraction of the maximum possible number of edges. Thus, while the previous model is most appropriate for the study of dense graphs, our model is most appropriate for the study of bounded-degree graphs. In particular, we present randomized algorithms for testing whether an unknown bounded-degree graph is connected, k -connected (for k>1 ), cycle-free and Eulerian. Our algorithms work in time polynomial in 1/? , always accept the graph when it has the tested property, and reject with high probability if the graph is ? -far from having the property. For example, the 2-connectivity algorithm rejects (with high probability) any N -vertex d -degree graph for which more than ? dN edges need to be added in order to make the graph 2-edge-connected. In addition we prove lower bounds of Ω(\sqrt N ) on the query complexity of testing algorithms for the bipartite and expander properties.     

Property Testing in Bounded Degree Graphs

Abstract. We further develop the study of testing graph properties as initiated by Goldreich, Goldwasser and Ron. Loosely speaking, given an oracle access to a graph, we wish to distinguish the case when the graph has a pre-determined property from the case when it is ``far' from having this property. Whereas they view graphs as represented by their adjacency matrix and measure the distance between graphs as a fraction of all possible vertex pairs, we view graphs as represented by bounded-length incidence lists and measure the distance between graphs as a fraction of the maximum possible number of edges. Thus, while the previous model is most appropriate for the study of dense graphs, our model is most appropriate for the study of bounded-degree graphs. In particular, we present randomized algorithms for testing whether an unknown bounded-degree graph is connected, k -connected (for k>1 ), cycle-free and Eulerian. Our algorithms work in time polynomial in 1/ɛ , always accept the graph when it has the tested property, and reject with high probability if the graph is ɛ -far from having the property. For example, the 2-connectivity algorithm rejects (with high probability) any N -vertex d -degree graph for which more than ɛ dN edges need to be added in order to make the graph 2-edge-connected. In addition we prove lower bounds of Ω(\sqrt N ) on the query complexity of testing algorithms for the bipartite and expander properties.     

Space Complexity Vs. Query Complexity

Combinatorial property testing deals with the following relaxation of decision problems: Given a fixed property and an input x, one wants to decide whether x satisfies the property or is “far” from satisfying it. The main focus of property testing is in identifying large families of properties that can be tested with a certain number of queries to the input. In this paper we study the relation between the space complexity of a language and its query complexity. Our main result is that for any space complexity s(n) ≤ log n there is a language with space complexity O(s(n)) and query complexity 2^Ω(s(n)). Our result has implications with respect to testing languages accepted by certain restricted machines. Alon et al. [FOCS 1999] have shown that any regular language is testable with a constant number of queries. It is well known that any language in space o(log log n) is regular, thus implying that such languages can be so tested. It was previously known that there are languages in space O(log n) that are not testable with a constant number of queries and Newman [FOCS 2000] raised the question of closing the exponential gap between these two results. A special case of our main result resolves this problem as it implies that there is a language in space O(log log n) that is not testable with a constant number of queries. It was also previously known that the class of testable properties cannot be extended to all context-free languages. We further show that one cannot even extend the family of testable languages to the class of languages accepted by single counter machines.      

Approximating minimum independent dominating sets in wireless networks

We present the first polynomial-time approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth which are used to model wireless communication networks.The approach presented yields a robust algorithm, that is, it accepts any undirected graph as input, and returns a (1+ε)-approximate minimum independent dominating set, or a certificate showing that the input graph does not satisfy the bounded growth property.     

Testing input validation in Web applications through automated model recovery

Input validation is essential and critical in Web applications. It is the enforcement of constraints that any input must satisfy before it is accepted to raise external effects. We have discovered some empirical properties for characterizing input validation in Web applications. In this paper, we propose an approach for automated recovery of input validation model from program source code. The model recovered is represented in a variant of control flow graph, called validation flow graph, which shows essential input validation features implemented in programs. Based on the model, we then formulate two coverage criteria for testing input validation. The two criteria can be used to guide the structural testing of input validation in Web applications. We have evaluated the proposed approach through case studies and experiments.     

An O(n+m) Certifying Triconnnectivity Algorithm for?Hamiltonian Graphs

A graph is triconnected if it is connected, has at least 4 vertices and the removal of any two vertices does not disconnect the graph. We give a certifying algorithm deciding triconnectivity of Hamiltonian graphs with linear running time (this assumes that the cycle is given as part of the input). If the input graph is triconnected, the algorithm constructs an easily checkable proof for this fact. If the input graph is not triconnected, the algorithm returns a separation pair.     

Efficient subgraph isomorphism detection: a decomposition approach

Graphs are a powerful and universal data structure useful in various subfields of science and engineering. In this paper, we propose a new algorithm for subgraph isomorphism detection from a set of a priori known model graphs to an input graph that is given online. The new approach is based on a compact representation of the model graphs that is computed offline. Subgraphs that appear more than once within the same or within different model graphs are represented only once, thus reducing the computational effort to detect them in an input graph. In the extreme case where all model graphs are highly similar, the run-time of the new algorithm becomes independent of the number of model graphs. Both a theoretical complexity analysis and practical experiments characterizing the performance of the new approach are given     

Hierarchy Theorems for Property Testing

Referring to the query complexity of property testing, we prove the existence of a rich hierarchy of corresponding complexity classes. That is, for any relevant function q, we prove the existence of properties that have testing complexity Θ(q). Such results are proven in three standard domains often considered in property testing: generic functions, adjacency predicates describing (dense) graphs, and incidence functions describing bounded-degree graphs. While in two cases, the proofs are quite straightforward, and the techniques employed in the case of the dense graph model seem significantly more involved. Specifically, problems that arise and are treated in the latter case include (1) the preservation of distances between graph under a blow-up operation and (2) the construction of monotone graph properties that have local structure.     

Linear-time algorithm for generating c-isolated bicliques

Bicliques are widely used to solve various real-world problems encountered in bio-informatics, data mining and networks. We consider c-isolated bicliques, a variation of bicliques. The c-isolated bicliques can model communities in social and biological networks. We propose an efficient algorithm to generate all c-isolated maximal bicliques in a given bipartite graph. Our algorithm exploits underlying properties of an isolated biclique to trim the input graph. Furthermore, the algorithm deploys the vertex cover enumeration algorithm based on fixed parameter tractability and lists all maximal c-isolated bicliques in linear time (in terms of graph size), for constant c.