The method is based on the preliminary transformation of the traditionally used matrices or adjacency lists in the graph theory into refined projections free from redundant information, and their subsequent use in constructing shortest paths. Unlike adjacency matrices and lists based on enumerating binary adjacency relations, the refined projection is based on enumerating more complex relations: simple paths from a given graph vertex that are shortest. The preliminary acquisition of such projections reduces the algorithmic complexity of applications using them and improves their volumetric and real-time characteristics to linear ones for a pair of vertices. The class of graphs considered is extended to mixed graphs.

翻译：该方法基于图论中传统使用的邻接矩阵或邻接列表的初步转换，将其转化为剔除冗余信息的精细化投影，并利用这些投影构建最短路径。与基于枚举二元邻接关系的邻接矩阵和列表不同，精细化投影基于枚举更复杂的关系：从给定图顶点出发的最短简单路径。预先获取此类投影可降低使用它们的应用的算法复杂度，并使其在顶点对上的体积特性和实时特性提升至线性水平。所考虑的图类扩展至混合图。