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

TL;DR

This paper corrects a previously proposed linear time algorithm for covering line segments with two squares, increasing the complexity to quadratic time due to identified bugs.

Contribution

It provides a corrected version of the original algorithm, fixing bugs and establishing an $O(n^2)$ time complexity for the LHIT problem.

Findings

Original linear time algorithm was flawed

Corrected algorithm runs in $O(n^2)$ time

Ensures all line segments are hit by two congruent squares

Abstract

In the paper "Linear time algorithm to cover and hit a set of line segments optimally by two axis-parallel squares", TCS Volume 769 (2019), pages 63--74, the LHIT problem is proposed as follows: For a given set of non-intersecting line segments ${\cal L} = \{\ell_1, \ell_2, \ldots, \ell_n\}$ in $I\!\!R^2$, compute two axis-parallel congruent squares ${\cal S}_1$ and ${\cal S}_2$ of minimum size whose union hits all the line segments in $\cal L$, and a linear time algorithm was proposed. Later it was observed that the algorithm has a bug. In this corrigendum, we corrected the algorithm. The time complexity of the corrected algorithm is $O(n^2)$.