通讯网络的极小费用树

The Minimal Cost Tree of Communication Network

本文针对ＭＣＭ９１问题Ｂ所给的９个通讯站，建立路径最短的数学模型，然后根据虚设站与路径的相互关系，以合并或分解虚设站为线索逐渐修改模型，最后确定的模型费用为１３４．８４，比美国马里兰州里斯勃莱州立大学数学科学系（ＭＣＭ的Ｄｉｒｅｃｔｏｒ）Ｂ．Ａ．Ｆｕｓａｒｏ提供的原文的费用少１．０５．本文新颖之处是改进图论中求最小生成树的方法，创造性地给出一个解决实际问题的新思路．

This artical has made a shortest path of mathematical model to the nine communication station given by MCM91 problem B, according to the relation of the imaginary station and path, modify model through compositing or decompositing imaginary station, confirm model cost in 134 84 at last. It is 1 05 little than the artical given by B.A. Fusaro mathematical department of Shalisibelai university in Mulilan state USA. This artical improved the way to produce the minimal generating tree in the graph theory and produced a new way to solve practical problem creatively.