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We present some fundamental structural properties for minimum length networks (known as Steiner minimum trees) interconnecting a given set of points in an environment in which edge segments are restricted to λ uniformly oriented directions. We show that the edge segments of any full component of such a tree contain a total of at most four directions if λ is not a multiple of 3, or six directions if λ is a multiple of 3. This result allows us to develop useful canonical forms for these full components. The structural properties of these Steiner minimum trees are then used to resolve an important open problem in the area: does there exist a polynomial time algorithm for constructing a Steiner minimum tree if the topology of the tree is known? We obtain a simple linear time algorithm for constructing a Steiner minimum tree for any given set of points and a given Steiner topology. 相似文献
104.
The virtual backbone is an approach for solving routing problems in ad-hoc wireless networks. The virtual backbone approach
features low latency, moderate routing overhead and is a hybrid scheme that uses the table-driven and on-demand routing protocols.
This work presents a distributed virtual backbone development scheme for ad-hoc wireless networks. Using clustering, distributed
labeling and heuristic Steiner tree techniques, our scheme outperforms other schemes in terms of the size and stability of
the virtual backbone and the virtual backbone change rate. Experimental results demonstrate that our scheme has lower overhead
than traditional table-driven and on-demand routing schemes.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
105.
学科建设是高校发展的核心, 随着高校学科建设的不断深入与强化, 学科建设信息持续增加, 且以离散的文件组织形式难以对学科建设成果进行高效的管理, 不利于后续分析与评估工作的开展. 针对此问题, 对学科建设知识图谱的构建及相关应用进行了研究. 首先通过BERT-BiLSTM-CRF模型对学科建设文本进行事件抽取, 并使用爬虫进行相关知识的补充. 然后选择属性图模型存储知识, 完成学科建设知识图谱的初步构建. 基于构建好的知识图谱, 搭建了学科建设可视化系统, 并引入最小斯坦纳树算法实现智能问答应用. 最后, 通过对学科建设事件抽取与智能问答方法进行实验分析, 验证了本文所提出方法的有效性. 相似文献
106.
In this paper, we consider a fiber routing problem arising from the design of optical transport networks. The problem is to find an optimal routing of multiple rings and an optimal location of wavelength division multiplexed (WDM) systems for carrying demand traffic. This problem can be conceptualized as a Steiner (multiple) ring problem with link capacity constraints. We formulate the problem as a mixed-integer programming model and develop a new branch-and-cut procedure along with preprocessing routines and valid inequalities for optimally solving the problem. Exploiting the inherent special structures of the formulation, we focus on developing strong valid inequalities and devising an effective Tabu search heuristic for solving large-scale problems. Computational results indicate that preprocessing rules and valid inequalities provide a tight lower bound, and in turn reduce the effort required to solve the problem within the framework of the branch-and-cut procedure. Moreover, the proposed Tabu search heuristic works quite well for solving large-scale problems. Motivated by promising computational results, we provide insights into implementing the proposed branch-and-cut procedure for deploying fiber optic networks in practice. 相似文献
107.
Hopfield neural network model for finding the shortest path between two nodes in a graph was proposed recently in some literatures. In this paper, we present a modified version of Hopfield model to a more general problem of searching an optimal tree (least total cost tree) from a source node to a number of destination nodes in a graph. This problem is called Steiner tree in graph theory, where it is proved to be a NP-complete. Through computer simulations, it is shown that the proposed model could always find an optimal or near-optimal valid solution in various graphs. 相似文献
108.
Given a node-weighted graph, the minimum-weighted dominating set (MWDS) problem is to find a minimum-weighted vertex subset such that, for any vertex, it is contained in this subset or it has a neighbor contained in this set. And the minimum-weighted connected dominating set (MWCDS) problem is to find a MWDS such that the graph induced by this subset is connected. In this paper, we study these two problems on a unit disk graph. A (4 +ε)-approximation algorithm for an MWDS based on a dynamic programming algorithm for a Min-Weight Chromatic Disk Cover is presented. Meanwhile, we also propose a (1 +ε)-approximation algorithm for the connecting part by showing a polynomial-time approximation scheme for a Node-Weighted Steiner Tree problem when the given terminal set is c-local and thus obtain a (5 +ε)-approximation algorithm for an MWCDS. 相似文献
109.
在三级系统双层门阵MALS2总体布线中,我们采用不等距网格宏单元模式总体布线图、节点勾链数据结构来支持总体布线。改进了收敛点的获取算法,提出了收敛方向概念,在此基础上实现了一个并行定向搜索的STEINER树算法,该算法特点是,各个顶点独立且并行地依据收敛方向朝各自的收敛点逼近,经过逐次合并形成STEINER树。该算法运行于三级系统双层门阵MALS2中,结果证明,该算法复杂度低,收敛时间短,结果令人满意。 相似文献
110.
We study the following fundamental problem in computational molecular biology: Given a set of DNA sequences representing some species and a phylogenetic tree depicting the ancestral relationship among these species, compute an optimal alignment of the sequences by the means of constructing a minimum-cost evolutionary tree. The problem is an important variant of multiple sequence alignment, and is widely known astree alignment. We design an efficient approximation algorithm with performance ratio 2 for tree alignment. The algorithm is then extended to a polynomial-time approximation scheme. The construction actually works for Steiner trees in any metric space, and thus implies a polynomial-time approximation scheme for planar Steiner trees under a given topology (with any constant degree). To our knowledge, this is the first polynomial-time approximation scheme in the fields of computational biology and Steiner trees. The approximation algorithms may be useful in evolutionary genetics practice as they can provide a good initial alignment for the iterative method in [23].Supported in part by NSERC Operating Grant OGP0046613.Supported in part by NSERC Operating Grant OGP0046613 and a Canadian Genome Analysis and Technology Research Grant.Supported in part by US Department of Energy Grant DE-FG03-90ER6099. 相似文献