中文摘要：

研究Hamming距离下的最短路改进问题的性质，并给出一个求解Hamming距离下的最短路改进问题的近似算法：按照一定规则得到满足一定条件的树型图，求解相应的0-1整数规划问题．该研究有助于设计求解Hamruing距离下的最短路改进问题的有效的近似算法．

英文摘要：

The properties of the shortest path improvement problem under Hamming distance was investigated, and an approximation algorithm for solving this problem was given, where a tree diagram which met definite conditions was obtained according to definite rules and, then, the corresponding programming problem with integers 0-1. It was expected that the investigation in this paper could be useful for devising more efficient approximation algorithms for solving the shortest path improvement problems under Hamming distance.