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Based on ventilation network graph is rooted directed weighted graph, its' nature of minimum spanning tree is proposed. According to the dense of ventilation network graph, introduces heap to improve the Prim algorithm, gives C++ implementation for the algorithm, and finally gains the Prim algorithm based on heap is both suitable for dense graph and sparse graph by analyzing its' time complexity, so the algorithm can meet the requirement to seek the minimum spanning tree of ventilation network graph. Mine ventilation system composed of crisscross roadway is a complex system. Describes ventilation system by the method of graph theory, ventilation network is a ventilation system which is composed of line, point and its properties. At present, calculation of ventilation network commonly used by Scott-Hinsley method, which needs determine the minimum spanning tree of network graph at first. The minimal spanning tree of an undirected weighted graph is a typical problem of graph theory, scholars of the world have conducted considerable research on it until now. The ventilation network graph is a weighted directed graph, there is a few research on the minimal spanning tree of a directed weighted graph. In addition, researches on dense degree of ventilation network graph isn't enough, scholars only qualitatively consider that ventilation network graph is dense graph. For shorting the time of calculating ventilation network by minimal spanning tree, it needs improve the Prim algorithm that is based on ventilation network graph is a directed weighted graph and its dense degree.

Prim Algorithm Based on Heap for Finding Minimal Spanning Tree of Ventilation Network