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This paper investigates a cellular edge caching problem under a very large number of small base stations (SBSs) and users. In this ultra-dense edge caching network (UDCN), conventional caching algorithms are inapplicable as their complexity increases with the number of small base stations (SBSs). Furthermore, the performance of UDCN is highly sensitive to the dynamics of user demand and inter-SBS interference. To overcome such difficulties, we propose a distributed caching algorithm under aarXiv:1801.07367v2 fatcat:mmdkvdo7svb5hkcmsmy3nubh5q