We study three covering problems in the plane. Our original motivation for these problems come from trajectory analysis. The first is to decide whether a given set of line segments can be covered by up to four unit-sized, axis-parallel squares. The second is to build a data structure on a trajectory to efficiently answer whether any query subtrajectory is coverable by up to three unit-sized axis-parallel squares. The third problem is to compute a longest subtrajectory of a given trajectory that can be covered by up to two unit-sized axis-parallel squares.

中文翻译：

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用几个正方形覆盖一组线段

我们研究了飞机上的三个覆盖问题。我们对这些问题的最初动机来自轨迹分析。第一个是确定给定的一组线段是否可以被最多四个单位大小的轴平行正方形覆盖。第二种是在轨迹上建立数据结构，以有效地回答任何查询子轨迹是否可被多达三个单位大小的轴平行正方形覆盖。第三个问题是计算给定轨迹的最长子轨迹，该轨迹可以由最多两个单位大小的轴平行正方形覆盖。