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.

中文翻译：

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图测地数的算法上限

基于最短路径的图理论问题由于其理论重要性和适用性而成为研究的核心。本文讨论了大地测量数，它是简单连接图的全局度量，并且属于覆盖问题的路径：什么是顶点的最小基数集，以便其元素之间的所有最短路径都覆盖图的每个顶点。受到最近文献中精确的0-1整数线性规划形式主义的启发，我们提出了一种新的方法来以算法的方式获得大地测量数的上限。这些算法的效率在一系列结构不同的图上得到了证明。