The advantages of Wireless Sensor Networks can not only compensate for the limitation of the traditional monitoring technology, but also greatly enhance the accuracy and efficiency of data transmission. In data transmission, it is necessary and important to consider the construction of virtual backbone (VB) to improve efficiency and stability. In this paper, we focus on the problem of constructing VB with the goal of guaranteeing the routing cost based on VB and minimizing the size of VB. We firstly give the formal definition of our problem, the Minimum Virtual Backbone with Guaranteed Routing Cost (MVB-GRC). To solve MVB-GRC problem, we propose an algorithm, 3-Color Classifying, to clarify all the nodes’ roles in the constructed VB with three colors. And it is proved that the routing cost based on the obtained VB by our algorithm is no more than 4 times as the minimum cost, and the size of VB has a upper bound about the size of the minimum connected dominating set. To evaluate the performance, the extensive simulation experiments are conducted and analyzed in terms of the construction cost and the routing cost.

无线传感器网络的优势不仅可以弥补传统监测技术的局限性，而且可以大大提高数据传输的准确性和效率。在数据传输中，考虑虚拟主干（VB）的构造以提高效率和稳定性是必要且重要的。在本文中，我们着重于构造VB的问题，目的是保证基于VB的路由成本并最小化VB的大小。我们首先给出问题的正式定义，即保证路由成本的最小虚拟骨干网（MVB-GRC）。为了解决MVB-GRC问题，我们提出了一种三色分类算法，以用三种颜色阐明构造的VB中所有节点的角色。并证明了基于我们的算法得到的VB的路由开销是最小开销的不超过4倍，并且VB的大小在最小连通支配集的大小上有一个上限。为了评估性能，进行了广泛的仿真实验，并根据建造成本和布线成本进行了分析。