Transversals, colouring, matchings and covers

我的研究目标将是解决图和超图中的各种极值类型问题。超图H是由一组顶点V和一组超边E组成的抽象对象，使得E的每个元素都是V的子集。图就是其中每条(超)边的大小为2的超图。许多重要的理论和实践问题都可以用关于图或超图的基本问题来表示。我要解决的问题都可以用这个纯粹抽象的术语来描述，并且通常涉及具有某些特殊属性的分区。然而，在许多情况下，它们来自非常具体的问题。我最近从事的两个具体应用涉及互联网中的有效路由协议，以及开发用于在电力系统中执行自动故障恢复的有效方案。故障恢复是指在暴风雨或其他意外损坏电力线路或网络其他组件导致电力中断后，通过重新配置网络来恢复电网中的电力的过程。随着智能电网的发展，电力恢复等方面对电网运行自动化的需求越来越大。

The objectives of my research will be to solve various extremal-type problems in graphs and hypergraphs. A hypergraph H is an abstract object consisting of a set of vertices V and a set of hyperedges E such that each element of E is a subset of V. A graph is just a hypergraph in which every (hyper)edge has size 2. Many important problems, both theoretical and practical, can be expressed in terms of basic questions about graphs or hypergraphs. The problems I will address can all be stated in this purely abstract terminology, and usually involve partitions with certain special properties. However in many cases they come from very concrete problems. Two specific applications I have worked on recently involve effective routing protocols in the internet, and the development of effective schemes for performing automatic fault restoration in electrical power systems. Fault restoration is the process of restoring power in an electrical grid by reconfiguring the network, after a power failure caused by a storm or other accidental damage to power lines or other components of the network. With the development of the smart grid, the need for automation in power restoration and other aspects of network operation is becoming much greater.