移位交换网的最优路由算法

移位交换网是重要的互联网络之一 ,在并行计算中有着广泛应用 .然而 ,它缺少任意点对间的最短路由算法 .已有的路由算法都不能保证其任意节点对间都是最短路由 .文中给出了一个最短路由算法 ,也是最优路由算法 ,它使得从源节点到目的节点的任何信息都是沿最短路由传输 .同时 ,我们还得到了任意节点对间的距离公式     

求解通信网节点间全部路由的逻辑代数化算法

经典的D IJKSTRA和BELLM AN-F LOYD通信网络路由算法,只能根据特定网络参数得到最佳路由,却无法获得网络存在的全部可用路由,而通信网理论研究及网络管理等方面,往往需要获得节点之间的全部可用路由.研究出一种路由新算法,遵循逻辑代数运算规则、采用关联矩阵中行与行之间整合与删除方式计算,N个节点的网络只需N-1次整合及删除运算,就能得到源节点到任意节点两点之间全部路由结果.详细论证了算法的正确性与合理性,简介了算法的并行运算可行性及与经典路由算法的兼容性等问题.通过算例详细说明算法的计算过程,并验证其正确性.     

构建最小k 重控制集的概率算法

点集D ⊆ V (G) 称为图G 的k 重控制集, 如果D 满足V (G) - D 中任意结点在D 中至少有k 个邻居. 在无线网络中, 最小k 重控制集(MkDS) 用以构建健壮的虚拟骨干网. 构建虚拟骨干网是无线网络中最基本也是最重要的问题. 在本文中, 我们提出一种快速的分布式概率算法来构建k重控制集. 我们构建的k 重控制集的期望大小不超过最优解的O(k²) 倍. 算法的运行时间复杂度为O((Δ logΔ+log log n)n),其中Δ = max{|D(p)|}, D(p) 是以p 为中心半径为1 的圆盘中的结点, 最大值的比较范围是给定集合中所有的p 点.     

n维超立方体的层次结构模型

本文首次提出了 n维超立方体的层次结构模型 HHC,详细讨论了该结构中结点的分布及各结点的连接关系 .并利用 HHC,讨论了超立方体非对称比较模型的最优诊断算法 ,极大独立点集等问题     

树网络上f模式最优广播问题的线性算法

网络G的一个结点v上的一次广播是指从它将一个消息传递给若干相邻结点.所谓f模式广播,是指结点v在一次广播中至多向f(v)个相邻结点传递信息(f为给定的整值函数).假定每一次广播的执行时间为一单位.网络G的广播过程是广播的时间安排,使所有结点均获得消息.最优广播问题是求总时间最少的广播过程.在G是树网络情形,文献中已给出时间界为O(n2)的算法.本文给出线性时间的简捷算法.     

钻井布局模型

本文的关键思想是找出在变化中的不变量 .对于第一小题 ,作者发现可以把所有的点“移到”一个方格中 ,而它们相对网格结点的距离不变 ,这样问题就得到了大大的简化 .对于第二题 ,本文发现坐标变换时各点之间的欧氏距离不变 ,利用各点的距离关系 ,给出一系列的判定条件 ,最后用优化算法 (充要条件 )判定 .第二题的算法对于第三题也是通用的 ,因此第三题应用第二题的方法来解决     

交互式点云建模系统

设计和实现了一个用于车载激光扫描点云处理的交互式建模系统.其原理是:在真实建筑物激光扫描数据的基础上,通过RANSAC实现自动化点云几何特征提取预处理,采用交互引导的方式辅助特征提取,采用随机算法计算边界特征,并通过构建多边形边界邻接图,计算建筑物几何模型.除特征提取外,涉及到的计算都是实时的.与传统处理方法相比,该系统具有速度快、精度高等优点.     

连续可导函数类的最优拉格朗日插值

在构造拉格朗日插值算法时,插值结点的选择是十分重要的.给定一个足够光滑的函数,如果结点选择的不好,当插值结点个数趋于无穷时,插值函数不收敛于函数本身.例如龙格现象:对于龙格函数f(x)=1/1+25x^2,如果拉格朗日插值的结点取[-1,1]上的等距结点,那么逼近的误差会随着结点个数增多而趋于无穷大⑴,由此可知插值结点的选择尤为重要.     

局部剖分邻接冠图的谱（英文）

设G_1,G_2是两个简单连通图,图G_1,G_2的局部剖分邻接冠图G_1■G_2是指复制一个G_1和|V(G_1)|个G_2,图G_1的第i个点的邻点与复制的第i个图G2的每一个点相连接,然后在G_1每一条边上插入一个新的点而得到的图类.本文利用两个图G_1,G_2的邻接谱、Laplacian谱和无符号Laplacian谱刻画了局部剖分邻接冠图G_1■G_2的邻接谱、Laplacian谱和无符号Laplacian谱.另外,本文利用上述结果构造出了若干对邻接同谱图、Laplacian同谱图和无符号Laplacian同谱图.进一步地,本文也利用两个因子图G_1,G_2的Laplacian谱计算出了局部剖分邻接冠图G_1■G_2的生成树数目.     

一种特殊形式的二元插值问题

在一特殊线性空间上给出一个结点组适定的充分条件和增加结点保持适定的方法,并给出算法.     

Ad Hoc网络中基于时分的分布式QoS路由算法

捷径冲突是AdHvc网络中QoS路由特有的一种现象，它由WenjianShao在[2]中首次提出．本文进一步研究了捷径冲突现象，给出了一个更加准确的定义，且给出了一个基于时分的分布式QoS路由算法成功地避免了捷径冲突现象．本算法是基于TDMA的分布式算法，每个节点只需了解网络的局部信息即可．数据分析表明本算法预留的最大带宽比较接近AdHoc网络中所能用的最大带宽．     

Routing optimization in packet switching communication networks

For routing assignments a special model and an optimization algorithm are proposed. The efficiency of the routing assignments is evaluated by the average value of the total cost of delays for all packets in the network. It is the objective function. The main idea is that traffic, which is transmitted from the source node to the destination node, can be split between two or more logical paths. The minimum of the objective function can be found by varying the traffic on every path and simultaneously from all the source nodes to the destination nodes. If this approach is applied, then the objective function is nonseparable and nonlinear. Because its shape is unknown in advance, an adaptive nonlinear optimization algorithm is proposed. For evaluating its efficiency a special set of test functions has been used.     

Routing trains through a railway station based on a node packing model

In this paper, we describe the problem of routing trains through a railway station. This routing problem is a subproblem of the automatic generation of timetables for the Dutch railway system. The problem of routing trains through a railway station is the problem of assigning each of the involved trains to a route through the railway station, given the detailed layout of the railway network within the station and given the arrival and departure times of the trains. When solving this routing problem, several aspects such as capacity, safety, and customer service have to be taken into account. In this paper, we describe this routing problem in terms of a weighted node packing problem. Furthermore, we describe an algorithm for solving this routing problem to optimality. The algorithm is based on preprocessing, valid inequalities, and a branch-and-cut approach. The preprocessing techniques aim at identifying superfluous nodes which can be removed from the problem instance. The characteristics of the preprocessing techniques with respect to propagation are investigated. We also present the results of a computational study in which the model, the preprocessing techniques and the algorithm are tested based on data related to the railway stations Arnhem, Hoorn and Utrecht CS in the Netherlands.     

Arc routing problems with time-dependent service costs

This paper studies an arc routing problem with capacity constraints and time-dependent service costs. This problem is motivated by winter gritting applications where the “timing” of each intervention is crucial. The exact problem-solving approach reported here first transforms the arc routing problem into an equivalent node routing problem. Then, a column generation scheme is used to solve the latter. The master problem is a classical set covering problem, while the subproblems are time-dependent shortest path problems with resource constraints. These subproblems are solved using an extension of a previously developed algorithm. Computational results are reported on problems derived from a set of classical instances of the vehicle routing problem with time windows.     

A New Multiobjective Dynamic Routing Method for Multiservice Networks: Modelling and Performance

There are potential advantages in formulating the routing problems in modern multiservice networks as multiple objective problems. This paper presents a novel hierarchical bi-level multiobjective dynamic routing model for multiservice networks. It is based on a bi-objective shortest path algorithm, with dynamically adapted soft-constraints, to compute alternative paths for each node pair and on a heuristic to synchronously select alternative routing plans for the network in a dynamic alternative routing context. It is a routing method which periodically changes alternative paths as a function of periodic updates of certain QoS related parameters obtained from real-time measurements. The performance of the proposed routing method is compared with two reference dynamic routing methods namely RTNR and DAR by means of a discrete-event simulator.A previous short version of this work was presented at INOC’03 (International Network Optimisation Conference). Work partially supported by programme POSI of the III EC programme cosponsored by FEDER and national funds.     

Autonomous localization based energy saving mechanism in indoor MANETs using ACO

The biggest challenge in MANETs is to find most efficient routing due to the changing topology and energy constrained battery operated computing devices. It has been found that Ant Colony Optimization (ACO) is a special kind of optimization technique having characterization of Swarm Intelligence (SI) which is highly suitable for finding the adaptive routing for such a type of volatile network. The proposed ACO routing algorithm uses position information and energy parameters as a routing metric to improve the performance and lifetime of network. Typical routing protocols have fixed transmission power irrespective of the distance between the nodes. Considering limiting factors, like small size, limited computational power and energy source, the proposed solution excludes use of GPS for identifying the distance between nodes for indoor MANETs. The distance between nodes can be determined by using Received Signal Strength Indicator (RSSI) measurements. Thus, an intelligent ACO routing algorithm with location information and energy metric is developed to adaptively adjust the transmission power and distribute the load to avoid critical nodes. Proposed Autonomous Localization based Eligible Energetic Path_with_Ant Colony Optimization (ALEEP_with_ACO) algorithm ensures that nodes in the network are not drained out of the energy beyond their threshold, as the load is shared with other nodes, when the energy of a node in the shortest path has reached its threshold. Hence, the total energy expenditure is reduced, thus prolonging the lifetime of network devices and the network. We simulated our proposal and compared it with the classical approach of AODV and other biological routing approaches. The results achieved show that ALEEP_with_ACO presents the best Packet Delivery Ratio (PDR), throughput and less packet drop specially under high mobility scenarios.     

PORA: A Physarum-inspired obstacle-avoiding routing algorithm for integrated circuit design

The plasmodium of Physarum polycephalum, a large, amoeboid cell, has attracted much attention recently due to its intelligent behaviors in pathfinding, danger avoidance, and network construction. Inspired by the biological behaviors of this primitive organism, in this study, we explore the optimization capability of Physarum polycephalum systematically and present the first Physarum-inspired obstacle-avoiding routing algorithm for the physical design of integrated circuits. We simulate the foraging behaviors of Physarum polycephalum using a novel nutrition absorption/consumption mathematical model, thereby presenting an efficient routing tool called Physarum router. With the proposed routing approach, for a given set of pin vertices and a given set of on-chip functional modules, a rectilinear Steiner minimal tree connecting all the pin vertices while avoiding the blockage of functional modules can be constructed automatically. Furthermore, several heuristics including a divide-and-conquer strategy, a non-pin leaf node pruning strategy, a dynamic parameter strategy, etc., are integrated into the proposed algorithm to fundamentally improve the performance of the Physarum router. Simulation results on multiple benchmarks confirm that the proposed algorithm leads to shorter wirelength compared with several state-of-the-art methods.     

New exact method for large asymmetric distance-constrained vehicle routing problem

In this paper we revise and modify an old branch-and-bound method for solving the asymmetric distance–constrained vehicle routing problem suggested by Laporte et al. in 1987. Our modification is based on reformulating distance–constrained vehicle routing problem into a travelling salesman problem, and on using assignment problem as a lower bounding procedure. In addition, our algorithm uses the best-first strategy and new tolerance based branching rules. Since our method is fast but memory consuming, it could stop before optimality is proven. Therefore, we introduce the randomness, in case of ties, in choosing the node of the search tree. If an optimal solution is not found, we restart our procedure. As far as we know, the instances that we have solved exactly (up to 1000 customers) are much larger than the instances considered for other vehicle routing problem models from the recent literature. So, despite of its simplicity, this proposed algorithm is capable of solving the largest instances ever solved in the literature. Moreover, this approach is general and may be used for solving other types of vehicle routing problems.     

Optimal solutions for routing problems with profits

In this paper, we present a branch-and-price algorithm to solve two well-known vehicle routing problems with profits, the Capacitated Team Orienteering Problem and the Capacitated Profitable Tour Problem. A restricted master heuristic is applied at each node of the branch-and-bound tree in order to obtain primal bound values. In spite of its simplicity, the heuristic computes high quality solutions. Several unsolved benchmark instances have been solved to optimality.