A 3.4713-approximation algorithm for the capacitated multicast tree routing problem

Given an underlying communication network represented as an edge-weighted graph G=(V,E), a source node sV, a set of destination nodes DV, and a capacity k which is a positive integer, the capacitated multicast tree routing problem asks for a minimum cost routing scheme for source s to send data to all destination nodes, under the constraint that in each routing tree at most k destination nodes are allowed to receive the data copies. The cost of the routing scheme is the sum of the costs of all individual routing trees therein. Improving on our previous approximation algorithm for the problem, we present a new algorithm which achieves a worst case performance ratio of , where ρ denotes the best known approximation ratio for the Steiner minimum tree problem. Since ρ is about 1.55 at the writing of the paper, the ratio achieved by our new algorithm is less than 3.4713. In comparison, the previously best ratio was .     

具有可行域内Steiner点寻优能力的配电网网架规划方法

文章研究配电网规划中网架规划的问题,提出了一种基于Steiner最小树的配电网网架规划新方法,解决了以往研究中没有考虑到的在规划中引入中间节点,并在可行域内寻优的问题。首先用路径描述方法建立了配电网网架规划的数学模型,然后将该数学模型转换成欧式Steiner最小树问题,并采用模拟退火算法求解。通过在算法中对Steiner点进行启发式搜索,实现了在可行域中搜索中间节点的方法,扩大了中间节点的选取范围,增大了搜索到全局最优解的概率。最后,通过算例分析验证了算法的性能和有效性。     

Simulation and Optimization of the Implementation Costs for the Last Mile of Fiber Optic Networks

The access net domain (last mile) still represents the bottleneck of present fiber optic network architectures. Although the investment volume in this domain definitely exceeds the costs of core- and distribution nets, network carriers hardly utilize intelligent planning tools for anticipatory investment decisions and cost optimization in this area. This article presents the methods behind a strategic planning and optimization tool which was developed in cooperation with renowned european city carriers. Based on real world geoinformation data a hierarchical optimization routine using methods of combinatorial optimization and graph theory allows a cost optimized simulation for the laying of fiber optic cables in the access net domain. Beside the used methodology an industrial benchmark project shows a typical scenario of application.     

A Polynomial Time Approximation Scheme for Minimum Cost Delay-Constrained Multicast Tree under a Steiner Topology

This paper is concerned with a restricted version of minimum cost delay-constrained multicast in a network where each link has a delay and a cost. Given a source vertex $s$ and $p$ destination vertices $t_1, t_2, \ldots, t_p$ together with $p$ corresponding nonnegative delay constraints $d_1, d_2, \ldots, d_p$, many QoS multicast problems seek a minimum cost multicast tree in which the delay along the unique $s$--$t_i$ path is no more than $d_i$ for $1 \le i \le p$. This problem is NP-hard even when the topology of the multicast tree is fixed. In this paper we show that every multicast tree has an underlying Steiner topology and that every minimum cost delay-constrained multicast tree corresponds to a minimum cost delay-constrained realization of a corresponding Steiner topology. We present a fully polynomial time approximation scheme for computing a minimum cost delay-constrained multicast tree under a Steiner topology. We also present computational results of a preliminary implementation to illustrate the effectiveness of our algorithm and discuss its applications.     

基于最小生成树的动态多播路由算法

提出了基于最小生成树的动态多播路由算法，称之为DPG（dynamic prim-based greedy multicast algorithm)算法，该算法属于不重组的动态多播路由算法。由于在所有节点都是多播节点时，最小生成树是最佳的，因此期望通过该算法产生的多播树的性能在合理的范围之内。结果表明DPG算法是一种平均无效率和最大无效度都在可接受的范围内的一种动态路由算法，尤其在多播节点密度较高时，它的平均无效率和最大无效度都较低。同时DPG算法的平均无效度对网络大小和网络平均节点度数不敏感，DPG算法的另一优点是时间复杂度低，它比贪婪算法和加权贪婪算法都快速。     

On the terminal Steiner tree problem

We investigate a practical variant of the well-known graph Steiner tree problem. In this variant, every target vertex is required to be a leaf vertex in the solution Steiner tree. We present hardness results for this variant as well as a polynomial time approximation algorithm with performance ratio ρ+2, where ρ is the best-known approximation ratio for the graph Steiner tree problem.     

The General Steiner Tree-Star problem

The Steiner tree problem is defined as follows—given a graph G=(V,E) and a subset X⊂V of terminals, compute a minimum cost tree that includes all nodes in X. Furthermore, it is reasonable to assume that the edge costs form a metric. This problem is NP-hard and has been the study of many heuristics and algorithms. We study a generalization of this problem, where there is a “switch” cost in addition to the cost of the edges. Switches are placed at internal nodes of the tree (essentially, we may assume that all non-leaf nodes of the Steiner tree have a switch). The cost for placing a switch may vary from node to node. A restricted version of this problem, where the terminal set X cannot be connected to each other directly but only via the Steiner nodes V?X, is referred to as the Steiner Tree-Star problem. The General Steiner Tree-Star problem does not require the terminal set and Steiner node set to be disjoint. This generalized problem can be reduced to the node weighted Steiner tree problem, for which algorithms with performance guarantees of Θ(lnn) are known. However, such approach does not make use of the fact that the edge costs form a metric. In this paper we derive approximation algorithms with small constant factors for this problem. We show two different polynomial time algorithms with approximation factors of 5.16 and 5.     

一种含浮动端点的斯坦纳树的构造算法

在集成电路的自动布图技术中，在完成布局过程，即各模块（或子电路单元）的拓扑位置确定以后，布线需要完成各电路模块之间的连接。斯坦纳树的构造问题可以应用于总体布线；如果考虑已有单元或连线的障碍，它也可以应用于详细布线。     

A note on the terminal Steiner tree problem

In 2002, Lin and Xue [Inform. Process. Lett. 84 (2002) 103-107] introduced a variant of the graph Steiner tree problem, in which each terminal vertex is required to be a leaf in the solution Steiner tree. They presented a ρ+2 approximation algorithm, where ρ is the approximation ratio of the best known efficient algorithm for the regular graph Steiner tree problem. In this note, we derive a simplified algorithm with an improved approximation ratio of 2ρ (currently ρ≈1.550, see [SODA 2000, 2000, pp. 770-790]).     

异质信息网络中最大路径连通Steiner分量查询算法

异质信息网络(HINs)是包含多种类型对象(顶点)和链接(边)的有向图,能够表达丰富复杂的语义和结构信息.HINs中的稠密子图查询问题,即给定一个查询点q,在HINs中查询包含q的稠密子图,已成为该领域的热点和重点研究问题,并在活动策划、生物分析和商品推荐等领域具有广泛应用.但现有方法主要存在以下两个问题:(1)基于模体团和关系约束查询的稠密子图具有多种类型顶点,导致其不能解决仅关注某种特定类型顶点的场景;(2)基于元路径的方法虽然可查询到某种特定类型顶点的稠密子图,但其忽略了子图中顶点之间基于元路径的连通度.为此,首先在HINs中提出了基于元路径的边不相交路径的连通度,即路径连通度;然后,基于路径连通度提出了k-路径连通分量(k-PCC)模型,该模型要求子图的路径连通度至少为k;其次,基于k-PCC模型提出了最大路径连通Steiner分量(SMPCC)概念,其为包含q的具有最大路径连通度的k-PCC;最后,提出一种高效的基于图分解的k-PCC发现算法,并在此基础上提出了优化查询SMPCC算法.大量基于真实和合成HINs数据的实验结果验证了所提出模型和算法的有效性和高效性.