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The present paper addresses the problem of cell planning for mobile radio networks. Existing solutions to such problems are based on heuristic approaches but these do not guarantee convergence to a true globally optimal solution. The use of a non global optimal solution can lead to significant unwarranted costs in the design of the network. In this paper, a 2-phase hierarchical algorithm is presented to find the optimal solution. Initially, the problem is developed in terms of a planar graph. In phase-I, the algorithm decomposes the targeted planar graph into a large number of smaller graphs. The sizes of such graphs are determined as a function of maximum transmitter power, operations and maintenance (O and M) constraints, allocated bandwidth and traffic distribution. Each small-size graph gives rise to a sub-problem. Each decomposed graph is then used to generate a number of admissible sub-graphs by applying various feasibility tests. In phase-II, an efficient optimization algorithm is used to select the combination of best subgraphs. The computational results obtained show the superiority of the proposed methodology to other known techniques, in terms of computational time and the quality of the solution obtained.