This study addresses the optimization problem with the objective of designing a pipe network. An underground pipe network for geographically dispersed customers must be designed with consideration of the many candidate roads below which pipes are laid. The layout and pipe sizes must then be determined to minimize the pipe network construction cost. However, this problem has attracted little research attention to date. In this study, we first formulate mathematical optimization models under the assumption of a single source node in a planar graph. We then find that the cost-minimized pipe network has a tree structure if the diameter of each pipe is a continuous variable. Thereafter, we develop an exact algorithm based on dynamic programming. The time complexity of the algorithm is polynomial in the number of nodes, but exponential in the number of faces covering all demand nodes for a planar graph. In addition, we propose a method for assigning commercial pipe diameters to the tree using a commercial solver. The computational results for a real-world gas distribution network show that our method provides an efficient solution. (C) 2019 Elsevier B.V. All rights reserved.