In this paper, we develop detailed algorithms for implementing the so-called Limited Column Generation procedure for Local Access Telecommunication Network(LATN) design problem. We formulate the problem into a tree-partitioning problem with an exponential number of variables. Its linear programming relaxation has all integral vertices, and can be solved by the Limited Column Generation procedure in just n pivots, where n is the number of nodes in the network. Prior to each pivot. an entering variable is selected by detecting the Locally Most Violated(LMV) reduced cost, which can be obtained by solving a subproblem in pseudo-polynomial time. A critical step in the Limited Column Generation is to find all the LMV reduced costs. As dual variables are updated at each pivot, the reduced costs have to be computed in an on-line fashion. An efficient implementation is developed to execute such a task so that the LATN design problem can be solved in O(n$^2$H), where H is the maximum concentrator capacity. Our computational experiments indicate that our algorithm delivers an outstanding performance. For instance, the LATN design problem with n＝150 and H＝1000 can be solved in approximately 67 seconds on a SUN SPARC 1000 workstation.