### Abstract

We give a polynomial-time approximation scheme for the unique unit-square coverage problem: given a set of points and a set of axis-parallel unit squares, both in the plane, we wish to find a subset of squares that maximizes the number of points contained in exactly one square in the subset. Erlebach and van Leeuwen [9] introduced this problem as the geometric version of the unique coverage problem, and the best approximation ratio by van Leeuwen [21] before our work was 2. Our scheme can be generalized to the budgeted unique unit-square coverage problem, in which each point has a profit, each square has a cost, and we wish to maximize the total profit of the uniquely covered points under the condition that the total cost is at most a given bound.

Original language | English |
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Pages (from-to) | 25-39 |

Number of pages | 15 |

Journal | Computational Geometry: Theory and Applications |

Volume | 51 |

DOIs | |

Publication status | Published - 2016 Jan |

### Keywords

- Dynamic programming
- Polynomial-time approximation scheme
- Shifting strategy
- Unique coverage problem

### ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics

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## Cite this

*Computational Geometry: Theory and Applications*,

*51*, 25-39. https://doi.org/10.1016/j.comgeo.2015.10.004