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This paper proposes the VisibilityCluster algorithm for efficient visibility approximation and representation in many-light rendering. By carefully clustering lights and shading points, we can construct a visibility matrix that exhibits good local structures due to visibility coherence of nearby lights and shading points. Average visibility can be efficiently estimated by exploiting the sparse structure of the matrix and shooting only few shadow rays between clusters. Moreover, we can use the estimated average visibility as a quality measure for visibility estimation, enabling us to locally refine VisibilityClusters with large visibility variance for improving accuracy. We demonstrate that, with the proposed method, visibility can be incorporated into importance sampling at a reasonable cost for the many-light problem, significantly reducing variance in Monte Carlo rendering. In addition, the proposed method can be used to increase realism of local shading by adding directional occlusion effects. Experiments show that the proposed technique outperforms state-of-the-art importance sampling algorithms, and successfully enhances the preview quality for lighting design.