Graph theoretical problems based on shortest paths are at the core of research due to their theoretical importance and applicability. This paper deals with the geodetic number which is a global measure for simple connected graphs and it belongs to the path covering problems: what is the minimal-cardinality set of vertices, such that all shortest paths between its elements cover every vertex of the graph. Inspired by the exact 0-1 integer linear programming formalism from the recent literature, we propose a new methods to obtain upper bounds for the geodetic number in an algorithmic way. The efficiency of these algorithms are demonstrated on a collection of structurally different graphs.

翻译：基于最短路径的图形理论问题,由于其理论重要性和适用性,是研究的核心。本文涉及大地测量数字,它是简单连接图形的全球测量标准,它属于覆盖问题的途径:什么是最小的心血管脊椎组,因此其元素之间的所有最短路径都覆盖了图形的每一个顶点。根据最近文献中准确的 0-1 整数线性编程形式学,我们提出了一个新方法,以算法方式获取大地测量数字的上界。这些算法的效率在结构上不同的图表中显示出来。