To solve connected dominating problem, it is necessary to find minimum connected dominating set (MCDS for short). However, to find MCDS is NP-hardness. So, a graph model called interval graph is constructed from nodes of related network. Two greedy algorithms with linear (or polynomial time) are used to find MCDS on proper interval graph (or interval graph), and have I approximation ratio on the graphs. And spanning trees are constructed and used to validate the correctness and effectiveness of corresponding algorithms.