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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 its boundary 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. The 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 optimization version. For the min-max problem, we present an O(n^2 n)arXiv:1107.1012v1 fatcat:b472zaxdkncldlszshrfgbn5sq