节点约束型最短路径的几何代数算法

面向网络分析应用中复杂条件约束下的最短路径求解问题，引入几何代数进行网络分析算法构造.建立了基于几何代数的网络模型和双边搜索算法，以寻找经过指定必经节点且弧段最少的最短路径求解为例，进行了算法实现.基于道路网络数据的分析显示，本算法利用外积运算直接判断约束节点，算法具有更好的通用性和较少的路径遍历次数，且在多对多路径求解及多用户并行求解上具有优势.

Geometric Algebra-Based Algorithm for Solving Nodes Constrained Shortest Path

Focusing on the solving of the shortest paths in the conditions of complicated constraints for network analysis and application,geometric algebra is used to develop the network analysis algorithms.We built a network model and bilateral search algorithms based on the multivector representation and multidimensional operators of geometric algebra.Then,we implemented the algorithm by taking the example of finding the shortest paths that pass the specified necessary nodes and the least segments.According to the experiment analysis of the road network data,this algorithm can directly estimate the constrained nodes by applying the outer algorithm and has better versatility and less path traversal times.Moreover,this algorithm has an advantage on many-to-many path solution and multi-user parallel solution.