Minimizing the Aggregate Movements for Interval Coverage
We consider an interval coverage problem. Given n intervals of the same length on a line L and a line segment B on L, we wish to move the intervals along L such that every point of B is covered by at least one interval and the sum of the moving distances of all intervals is minimized. As a basic geometry problem, it also has applications in mobile sensor barrier coverage. The previous work solved the problem in \(O(n^2)\) time. In this paper, we present an \(O(n\log n)\) time algorithm.
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