最短路径问题

Finding the shortest path in a directed network is the basic problem in graph theory.

有向图中的最短路径问题是图论应用的基本问题，对很多实际问题很有指导意义。

The shortest-paths problem involves a weighted, possibly directed graph described by the set of edges and vertices { E , V }.

最短路径问题包含一个承受的重力，尽可能地直的曲线图，该图由一组优势线和顶点{ E ， V }描述。

How to provide route to meet the driver's multiple psychological expectations is the key problem of navigation system. The essence of this problem is resource constrained shortest path problem, which belongs to NP-C problems and can not be solved with the traditional shortest path algorithm.

提供满足驾驶员多个心理期望的路径是导航系统该解决的关键问题，其本质是资源约束最短路径问题，属于NP难问题，无法使用传统的最短路径算法解决。

The shortest path problem has been widely applied in real-life and has been extensively studied by many researchers.

最短路径问题在现实生活中有着广泛应用，许多专家学者对此问题进行了深入研究。

The problem on the shortest path is a basic problem of traffic networks analysis system. It has been discussed widely and deeply.

最短路径问题是交通网络分析系统的一个基本问题，在理论上得到了广泛深入的研究。

Searching shortest path is one of the most important questions in a network from a node to another.

最短路径问题是在给定的网络图中寻找出一条从起始点到目标点之间的最短路径。

Machine study algrithm for artificial intelligence and neural network, it can solve the problem of shortest route

人工智能及神经网络的机器学习算法，经典的遗传算法，在实际中可以解决选路问题及最短路径问题。

This can be established without a map to the right, then seeking the shortest route into the problem for a map of the rest of Vertex Vertex all the shortest path probl

这样就可以建立一个无向有权图，那么求最短的运输路线问题就转化为求图中一顶点到其余各个顶点的最短路径问题了。

Key Words: Dynamic network, Time dependent vehicle route problem, Time dependent shortest path problem, route construction algorithm, Genetic Algorithm, Ant Colony Optimization Algorithms, Component-based software development

最后，对本文的主要工作和研究成果进行了总结，并简要讨论了进一步的研究方向。关键词：动态路网，时间依赖型车辆路径问题，动态最短路径问题，构造算法，遗传算法，蚁群算法，组件式开发

Image segmentation based on the graph concept is analyzed in our thesis, a boundary finding problem is formulated as a shortest-path problem in a graph, then a watershed algorithm based ort image foresting transfonn is introduced, which is a unified and efficient approach for simplifying image processing problems to a minimum-cost path forest problem .

将图的概念应用于图像分割的研究中，把边界发现问题归结为图中的最短路径问题，从而引入了一种基于图像森林化变换(Image Foresting Transform，该方法是把图像处理问题简化为在图中求解最短路径森林问题的一种统一有效的方法)的分水岭算法，并分析了平滑滤波、梯度阈值在图像分割中的作用。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

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