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The $k$-coverage problem is to find the minimum number of disks such thateach point in a given plane is covered by at least $k$ disks. Under unit diskcondition, when $k$=1, this problem has been solved by Kershner in 1939.However, when $k > 1$, it becomes extremely difficult. One tried to tackle thisproblem with different restrictions. In this paper, we restrict ourself tocongruent Voronoi polygon, and prove the minimum density of the two-coveragewith such a restriction. Our proof is simpler and more rigorous than that givenrecently by Yun et al.

Two-Fold Circle-Covering of the Plane under Congruent Voronoi Polygon Conditions