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We study, by numerical simulation, the compaction dynamics of frictional hard disks in two dimensions, subjected to vertical shaking. Shaking is modeled by a series of vertical expansion of the disk packing, followed by dynamical recompression of the assembly under the action of gravity. The second phase of the shake cycle is based on an efficient event-driven molecular-dynamics algorithm. We analyze the compaction dynamics for various values of friction coefficient and coefficient of normal restitution. We find that the time evolution of the density is described by ρ (t) = ρ -Δρ Eα [- (t/τ)α], where Eα denotes the Mittag-Leffler function of order 0<α<1. The parameter τ is found to decay with tapping intensity Γ according to a power law τ/ Γ-γ, where parameter γ is almost independent on the material properties of grains. Also, an expression for the grain mobility during the compaction process has been obtained. We characterize the local organization of disks in terms of contact connectivity and distribution of the Delaunay "free" volumes. Our analysis at microscopic scale provides evidence that compaction is mainly due to a decrease of the number of the largest pores. An interpretation of the memory effects observed for a discontinuous shift in tapping intensity Γ is provided by the analysis of the time evolution of connectivity numbers and volume distribution of pores. © 2006 The American Physical Society.