Applications of graph theory

我有两个主要的项目。一个是尽快找到一个图的最小圈基。最小的圈基被用来研究网络中的圈，特别是当网络通向一组方程时。更小的基会产生更简单的方程来求解。它的应用包括电子网络、结构工程、地铁系统调度、研究新陈代谢路径、拓扑学。另一个项目是子句树的研究。所有这些都提供了一种方法来在简单的图中表示一组有限的逻辑证明，可以在计算机中表示。然后可以编写计算机程序，从已知的公理出发，构造和操作子句树以找到定理的证明。使用这种自动化定理证明器的新结果还很少，但这样的系统被用于许多人工智能应用。子句树如何能够比其他使用计算机进行推理的方法更快地找到证据？

I have two major projects.  One is to find as quickly as possible the minimum cycle basis of a graph.  Cycle bases are used to study cycles in networks, especially when the networks lead to sets of equations.  Smaller bases produce simpler equations to be solved.  Applications include electrical networks, structural engineering, scheduling subway systems, studying metabolic pathways, in topology.       The other project is the study of clause trees.  These give a way to represent a restricted set of logical proofs in simple diagrams, that can be represented in a computer.  Then computer programs can be written, starting from known axioms, to construct and manipulate clause trees to find proofs of theorems. Few new results have been found using such automated theorem provers yet, but such systems are used in many artifical intelligence applications.  Can clause trees be used to find proofs faster than other methods of reasoning with computers?