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Given n points in a circular region C in the plane, we study the problems of moving the n points to the boundary of G to form a regular n-gon such that the maximum (min-max) or the sum (min-sum) of the Euclidean distances traveled by the points is minimized. These problems have applications, e.g., in mobile sensor barrier coverage of wireless sensor networks. The min-max problem further has two versions: the decision version and the optimization version. For the min-max problem, we present andoi:10.1007/s00453-013-9857-1 fatcat:wkgw4s3wkbbkfhmeplaslfpftm