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With various wireless technologies developed, a ubiquitous and integrated architecture is envisioned for future wireless communication. An important optimization issue in such an integrated system is how to minimize the overall communication cost by intelligently utilizing the available heterogeneous wireless technologies while, at the same time, meeting the quality-of-service requirements of mobile users. In this paper, we first identify the cost-minimization (CM) problem to be NP-hard. We then present an efficient minimum-cost data-delivery algorithm based on linear programming (LP), with various constraints, such as channel bandwidth, link costs, delay budgets, and user mobility, taken into consideration. In case of insufficient bandwidth for communication with the core network, prefetch is employed to fully utilize the wireless-network capacity. If multiple routes are available, a probability-based approach is taken for CM. Extensive simulations are carried out to evaluate the proposed CM scheme. Our results show that the proposed LP approach can effectively reduce the overall communication cost, with small overhead (< 3%) for signaling, computing, and handoff. We expect that minimum-cost data delivery will become imperative for the future heterogeneous wireless networks and the emerging 4G wireless systems.