2-重心问题及其反问题的研究

通过研究树上的具有非负权重的2-重心问题，得出了下面的结论：若顶点子集{a，b}包含于V是树的2-重心，在树上连接顶点a和顶点b有唯一的一条路，去掉路的中点所在的边，树分成两个子树，则a和b分别是所在子树的1重心．根据这个结论，提出了具体的算法，即树上的具有非负权重的2-重心可以通过在其子树上求1-重心来得到。树上的具有非负权重的2-重心问题的反问题，可以转化为线性规划模型求解，存在有效算法。

Studies on the 2-median Problem and Its Inverse Problem on a Tree

Based on the studies of the 2-median problem on a tree with non-negative weights, it is concluded that if the subset {a,b}lohtain in V is the 2 median of the tree, there exists an unique path in the tree joining vertex a with vertex b. Through deleting the edge on which the midpoint of the path lies, the tree is divided into two subtrees, then a and b are the 1-median of the two subtrees respectively. Based on this conclusion, a specific algorithm is proposed to solve the 2-median of the tree with non-negative weights; The inverse 2-meidan problem on a tree with non-negative weights can be translated into ＂a＂ linear programming model, which could be solved by an effective algorithm.