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1.
Depending on whether bidirectional links or unidirectional links are used for communications, the network topology under a
given range assignment is either an undirected graph referred to as the bidirectional topology, or a directed graph referred
to as the unidirectional topology. The Min-Power Bidirectional (resp., Unidirectional) k-Node Connectivity problem seeks a range assignment of minimum total power subject to the constraint that the produced bidirectional
(resp. unidirectional) topology is k-vertex connected. Similarly, the Min-Power Bidirectional (resp., Unidirectional) k-Edge Connectivity problem seeks a range assignment of minimum total power subject to the constraint the produced bidirectional
(resp., unidirectional) topology is k-edge connected.
The Min-Power Bidirectional Biconnectivity problem and the Min-Power Bidirectional Edge-Biconnectivity problem have been studied
by Lloyd et al. [23]. They show that range assignment based the approximation algorithm of Khuller and Raghavachari [18],
which we refer to as Algorithm KR, has an approximation ratio of at most 2(2 – 2/n)(2 + 1/n) for Min-Power Bidirectional Biconnectivity, and range assignment based on the approximation algorithm of Khuller and Vishkin [19],
which we refer to as Algorithm KV, has an approximation ratio of at most 8(1 – 1/n) for Min-Power Bidirectional Edge-Biconnectivity.
In this paper, we first establish the NP-hardness of Min-Power Bidirectional (Edge-) Biconnectivity. Then we show that Algorithm KR has an approximation ratio of at most 4 for both Min-Power Bidirectional Biconnectivity and Min-Power Unidirectional Biconnectivity,
and Algorithm KV has an approximation ratio of at most 2k for both Min-Power Bidirectional k-Edge Connectivity and Min-Power Unidirectional k-Edge Connectivity. We also propose a new simple constant-approximation algorithm for both Min-Power Bidirectional Biconnectivity
and Min-Power Unidirectional Biconnectivity. This new algorithm applies only to Euclidean instances, but is best suited for
distributed implementation.
A preliminary version of this work appeared in the proceedings of the 2nd International Conference on AD-HOC Network and Wireless
(Adhoc-Now 2003).
Research performed in part while visiting the Max-Plank-Institut fur Informatik.
Gruia Calinescu is an Assistant Professor of Computer Science at the Illinois Institute of Technology since 2000. He held postdoc or visiting
researcher positions at DIMACS, University of Waterloo, and Max-Plank Institut fur Informatik. Gruia has a Diploma from University
of Bucharest and a Ph.D. from Georgia Insitute of Technology. His research interests are in the area of algorithms.
Peng-Jun Wan has joined the Computer Science Department at Illinois Institute of Technology in 1997 and has been an Associate Professor
since 2004. He received his Ph.D. in Computer Science from University of Minnesota in 1997, M.S. in Operations Research and
Control Theory from Chinese Academy of Science in 1993, and B.S. in Applied Mathematics from Tsinghua University in 1990.
His research interests include optical networks and wireless networks. 相似文献
2.
一种支持QoS的拓扑自适应动态组播路由算法 总被引:3,自引:0,他引:3
YAM、QoSMIC、DSDMR等一类支持QoS的动态组播路由算法允许组播成员动态地加入和离开,同时为接收方提供多个可选择的组播接入路径,以满足不同应用的QoS需求。但这些算法普遍存在控制信令开销大和结点加入时延长,可扩展性不好等问题。本文在分析这些算法的基础上,提出改进的支持QoS的动态组播路由算法,即拓扑自适应动态组播路由(Topology Adaptive Dynamic Multicast Routing,TADMR)算法。该算法避免了以往算法中大部分盲目的路径搜索,并使结点加入时延不再受限于固定的等待时钟,而与网络拓扑相自适应。性能分析和仿真结果表明,该算法具有较低的控制信令开销和结点加入时延,适用于各种网络规模和群组规模,具有良好的可扩展性。 相似文献
3.
Paul J. Flory 《Polymer International》1985,17(2):96-102
The earliest investigations on rubber elasticity, commencing in the 19th century, were necessarily limited to phenomenological interpretations. The realisation that polymers consist of very long molecular chains. commencing c. 1930, gave impetus to the molecular theory of rubber elasticity (1932-). according to which the high deformability of an elastomer, and the elastic force generated by deformation, stem from the configurations accessible to long molecular chains. Theories of rubber elasticity put forward from 1934-1946 relied on the assumption that the junctions of the rubber network undergo displacements that are affine in macroscopic strain. The theory of James and Guth (1947) dispensed with this premise, and demonstrated instead that the mean positions of the junctions of a ‘phantom’ network consisting of Gaussian chains devoid of material properties are affine in the strain. The vital significance of the distinction between the actual distribution of chain vectors in a network and their distribution if the junctions would be fixed at their mean positions went unnoticed for nearly 30 years. Experimental investigations, commencing with the incisive work of Gee in 1946. revealed large departures from the relationship of stress to strain predicted by the theories cited. This discrepancy prompted extensive studies, theoretical and experimental, during succeeding years. Inquiry into the fundamentals of polymer networks, formed for example by interlinking very long polymer molecules, exposed the need to take account of network imperfections, typically consisting of chains attached at only one end to a network junction. Various means were advocated to make corrections for these imperfections. The cycle rank ζ of the network has been shown (1976) to be the fundamental measure of its connectivity, regardless of the junction functionality and pattern of imperfections. Often overlooked is the copious interpenetration of the chains comprising typical elastomeric networks. Theories that attempt to represent such networks on a lattice are incompatible with this universal feature. Moreover, the dense interpenetration of chains may limit the ability of junctions in real networks to accommodate the fluctuations envisaged in the theory of phantom networks. It was suggested in 1975 that departures from the form predicted for the elastic equation of state are due to constraints on the fluctuations of junctions whose effect diminishes with deformation and with dilation. Formulation of a self-consistent theory based on this suggestion required recognition of the non-affine connection between the chain vector distribution function and the macroscopic strain in a real network, which may partake of characteristics of a phantom network in some degree. Implementation of the idea was achieved through postulation of domains of constraint affecting the equilibrium distribution of fluctuations of network junctions from their mean positions. This led in due course to a theory that accounts for the relationship of stress to strain virtually throughout the ranges of strain accessible to measurement. The theory establishes connections between structure and elastic properties. This is achieved with utmost frugality in arbitrary parameters. 相似文献
4.
Lei Liu Ying Kong Hong Xu Jin P. Li Jin X. Dong Zhi Lin 《Microporous and mesoporous materials》2008,115(3):624-628
A three-dimensional zinc phosphate compound with DFT topology, designated as ZnPO4-EU1, has been synthesized by an ionothermal approach from the system HF-ZnO–P2O5-choline chloride-imidazolidone. Ethylenediamine, derived from decomposition of the imidazolidone component of the deep-eutectic solvent (DES) itself, is delivered to the synthesis and serves as an appropriate template for ZnPO4-EU1. Experiments in which the synthesis conditions were varied showed that ZnPO4-EU1 may be prepared over a wide molar ratio of P/Zn = 0.55–13.0. Powder X-ray diffraction patterns have been obtained at intervals to track the crystallization process of this material. The experimental data show that Zn3(PO4)2 · 4H2O (a dense phase) was first isolated from the DES after reaction for 1 h. Subsequently, the pure phase of ZnPO4-EU1 was obtained with increasing crystallization time from 12 h to 72 h. The experimental results show that the nucleation and crystallization take place with relatively low levels of solvent degradation, demonstrating that zinc phosphate with a three-dimensional framework can be synthesized by in situ generation of an appropriate template using an unstable DES at high temperatures (150–200 °C). 相似文献
5.
Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays 总被引:5,自引:0,他引:5
In this paper, we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time-varying communication delays. By employing a linear matrix inequality method, we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected. Particularly, several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time-varying communication delays. Numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results. 相似文献
6.
Education-driven research in CAD 总被引:1,自引:0,他引:1
We argue for a new research category, named education-driven research (EDR), which fills the gap between traditional field-specific research that is not concerned with educational objectives and research in education that focuses on fundamental teaching and learning principles and possibly on their customization to broad areas (such as mathematics or physics), but not to specific disciplines (such as CAD). The objective of EDR is to simplify the formulation of the underlying theoretical foundations and of specific tools and solutions in a specialized domain, so as to make them easy to understand and internalize. As such, EDR is a difficult and genuine research activity, which requires a deep understanding of the specific field and can rarely be carried out by generalists with primary expertise in broad education principles. We illustrate the concept of EDR with three examples in CAD: (1) the Split and Tweak subdivisions of a polygon and its use for generating curves, surfaces, and animations; (2) the construction of a topological partition of a plane induced by an arbitrary arrangement of edges; and (3) a romantic definition of the minimal and Hausdorff distances. These examples demonstrate the value of using analogies, of introducing evocative terminology, and of synthesizing the simplest fundamental building blocks. The intuitive understanding provided by EDR enables the students (and even the instructor) to better appreciate the limitations of a particular solution and to explore alternatives. In particular, in these examples, EDR has allowed the author to: (1) reduce the cost of evaluating a cubic B-spline curve; (2) develop a new subdivision curve that is better approximated by its control polygon than either a cubic B-spline or an interpolating 4-point subdivision curve; (3) discover how a circuit inclusion tree may be used for identifying the faces in an arrangement; and (4) rectify a common misconception about the computation of the Hausdorff error between triangle meshes. We invite the scientific community to encourage the development of EDR by publishing its results as genuine research contributions in peer-reviewed professional journals. 相似文献
7.
8.
M. Stolpe K. Svanberg 《International journal for numerical methods in engineering》2003,57(5):723-739
This paper deals with topology optimization of discretized continuum structures. It is shown that a large class of non‐linear 0–1 topology optimization problems, including stress‐ and displacement‐constrained minimum weight problems, can equivalently be modelled as linear mixed 0–1 programs. The modelling approach is applied to some test problems which are solved to global optimality. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
9.
空间桁架结构拓扑优化设计的线性规划方法 总被引:1,自引:0,他引:1
本文以杆件内力为设计变量,构造了多工况作用下空间桁架结构拓扑优化的线性规划模型,考虑了应力和位移约束,能够避免奇异最优拓扑和不稳定结构的产生。 相似文献
10.
基于混合遗传算法的树状注水管网拓扑优化 总被引:4,自引:1,他引:3
以投资最小为目标函数,以井间隶属关系的惟一性、连接注水井数量等限制为约束条件,建立了树状注水管网拓扑优化数学模型.根据模型特点,将优化问题分为分配层和几何层,分别采用遗传算法和非线性优化方法进行求解.并对遗传算法的操作过程进行了改进,调整了适应函数,采用随机多父辈适应函数值加权交叉和多种变异操作,结合了模拟退火算法,并给出了初温的确定方法,改进了选择复制操作,从而形成了混合遗传算法.该算法能够有效地提高收敛速度,避免早熟收敛.利用算例说明了该方法的有效性. 相似文献