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Coded caching is a problem where encoded broadcasts are used to satisfy usersrequesting popular files and having caching capabilities. Recent work byMaddah-Ali and Niesen showed that it is possible to satisfy a scaling number ofusers with only a constant number of broadcast transmissions by exploitingcoding and caching. Unfortunately, all previous schemes required the splittingof files into an exponential number of packets before the significant codinggains of caching appeared. The question of what can be achieved with polynomialsubpacketization (in the number of users) has been a central open problem inthis area. We resolve this problem and present the first coded caching schemewith polynomial (in fact, linear) subpacketization. We obtain a number oftransmissions that is not constant, but can be any polynomial in the number ofusers with an exponent arbitrarily close to zero. Our central technical tool isa novel connection between Ruzsa-Szem\'eredi graphs and coded caching.

Coded Caching with Linear Subpacketization is Possible using Ruzsa-Szem\'eredi Graphs