In this paper we have proposed a linear time algorithm for solving the minimum sharable-bandwidth tree construction problem. The public-shared network is a user generated infrastructure on which a user can access the Internet and transfer data from any place via access points with sharable bandwidth. Recently, the idea of constructing the SVC video streaming delivery system on public-shared network has been proposed. To send video stream from the stream server to clients on public-shared network, a tree structure is constructed. The problem of constructing a tree structure to serve the video streaming requests by using minimum amount of sharable bandwidth has been shown to be NP-hard. The previously published algorithms for solving this problem are either unable to find solutions frequently or less efficient. The experimental results showed that our algorithm is excellent both in the success rate of finding solutions and in the quality of solutions.