# Covering a set of line segments with a few squares

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.

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09/14/2017

### A linear time algorithm to cover and hit a set of line segments optimally by two axis-parallel squares

This paper discusses the problem of covering and hitting a set of line s...
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09/06/2021

### Disjoint axis-parallel segments without a circumscribing polygon

We construct a family of 17 disjoint axis-parallel line segments in the ...
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09/20/2019

### Corrigendum to: "Linear time algorithm to cover and hit a set of line segments optimally by two axis-parallel squares", Theoretical Computer Science 769 (2019) 63--74

In the paper "Linear time algorithm to cover and hit a set of line segme...
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06/05/2022

### Packing, Hitting, and Coloring Squares

Given a family of squares in the plane, their packing problem asks for t...
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12/20/2022

### Dominance for Containment Problems

In a containment problem, the goal is to preprocess a set of geometric o...
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08/30/2022

### Approximation Algorithm for Minimum p Union Under a Geometric Setting

In a minimum p union problem (MinpU), given a hypergraph G=(V,E) and an ...
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09/08/2017

### Balanced Line Separators of Unit Disk Graphs

We prove a geometric version of the graph separator theorem for the unit...