Applications of graph theory

我有两个主要项目。 一个是尽可能快地找到图的最小圈基。 循环基用于研究网络中的循环，特别是当网络导致方程组时。 较小的基产生更简单的方程来求解。 应用包括电气网络，结构工程，调度地铁系统，研究代谢途径，拓扑学。 另一个项目是研究子句树。 这些提供了一种方法来表示一组限制的逻辑证明在简单的图表，可以在计算机中表示。 然后，可以从已知的公理开始编写计算机程序，以构建和操作子句树来找到定理的证明。很少有新的结果已经发现使用这种自动定理证明，但这样的系统在许多人工智能应用程序中使用。 子句树能比其他计算机推理方法更快地找到证明吗？

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?