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Caching popular files at user equipments (UEs) provides an effective way toalleviate the burden of the backhaul networks. Generally, popularity-basedcaching is not a system-wide optimal strategy, especially for user mobilityscenarios. Motivated by this observation, we consider optimal caching withpresence of mobility. A cost-optimal caching problem (COCP) fordevice-to-device (D2D) networks is modelled, in which the impact of usermobility, cache size, and total number of encoded segments are all accountedfor. Compared with the related studies, our investigation guarantees that thecollected segments are non-overlapping, takes into account the cost ofdownloading from the network, and provides a rigorous problem complexityanalysis. The hardness of the problem is proved via a reduction from thesatisfiability problem. Next, a lower-bounding function of the objectivefunction is derived. By the function, an approximation of COCP (ACOCP)achieving linearization is obtained, which features two advantages. First, theACOCP approach can use an off-the-shelf integer linear programming algorithm toobtain the global optimal solution, and it can effectively deliver solutionsfor small-scale and mediumscale system scenarios. Second, and more importantly,based on the ACOCP approach, one can derive the lower bound of global optimumof COCP, thus enabling performance benchmarking of any suboptimal algorithm. Totackle large scenarios with low complexity, we first prove that the optimalcaching placement of one user, giving other users' caching placements, can bederived in polynomial time. Then, based on this proof, a mobility awareuser-by-user (MAUU) algorithm is developed. Simulation results verify theeffectivenesses of the two approaches by comparing them to the lower bound ofglobal optimum and conventional caching algorithms.

Cost-optimal caching for D2D networks with user mobility: Modeling, analysis, and computational approaches