# Packing Rotating Segments

## TL;DR

This paper proves the NP-hardness of a labeling problem for rotating maps and introduces a polynomial approximation scheme to solve it, extending to arbitrary label shapes.

## Contribution

It establishes NP-hardness for the rotating map labeling problem and provides a polynomial approximation algorithm, extending to general label shapes.

## Key findings

- NP-hardness of the rotating map labeling problem.
- A polynomial approximation scheme for the problem.
- Extension of the algorithm to arbitrary label objects.

## Abstract

We show that the following variant of labeling rotating maps is NP-hard, and present a polynomial approximation scheme for solving it. The input is a set of feature points on a map, to each of which a vertical bar of zero width is assigned. The goal is to choose the largest subsets of the bars such that when the map is rotated and the labels remain vertical, none of the bars intersect. We extend this algorithm to the general case where labels are arbitrary objects.