Both the arc operad and planar algebras are built from graphs on surfaces. Although similar in nature they were constructed with different aspects of geometry and applications in mind. With hindsight there is a striking similarity in one particular application. To elucidate this possible connection, we will proceed by introducing the arc operad and its discretization. The latter gives rise to actions on the Hochschild complex of a (Frobenius) algebra. These operations include Deligne's conjecture, its cyclic version and string topology. This discretization is also what is closely related to planar diagrams as we shall discuss.