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  introduced this problem as the geometric version of the unique coverage problem, and the best approximation ratio by van Leeuwen  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.
ASJC Scopus subject areas
- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics