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In this paper, we propose a terrestrial-satellite network (TSN) architecture to integrate the ultra-dense low earth orbit (LEO) networks and the terrestrial networks to achieve efficient data offloading. In TSN, each ground user can access the network over C-band via a macro cell, a traditional small cell, or a LEO-backhauled small cell (LSC). Each LSC is then scheduled to upload the received data via multiple satellites over Ka-band. We aim to maximize the sum data rate and the number of accessed users while satisfying the varying backhaul capacity constraints jointly determined by the LEO satellite-based backhaul links. The optimization problem is then decomposed into two closely connected subproblems and solved by our proposed matching algorithms. The simulation results show that the integrated network significantly outperforms the non-integrated ones in terms of the sum data rate. The influence of the traffic …