Straightening out planar poly-line drawings

TL;DR

This paper proves that any y-monotone poly-line drawing can be straightened while preserving y-coordinates and height, but width may need to increase exponentially, and y-monotonicity is essential for this process.

Contribution

It introduces a method to straighten y-monotone poly-line drawings without changing height, highlighting the necessity of y-monotonicity and analyzing width requirements.

Findings

Straightening preserves y-coordinates and height.

Exponential width increase may be necessary.

Non y-monotone drawings cannot always be straightened without height increase.

Abstract

We show that any $y$-monotone poly-line drawing can be straightened out while maintaining $y$-coordinates and height. The width may increase much, but we also show that on some graphs exponential width is required if we do not want to increase the height. Likewise $y$-monotonicity is required: there are poly-line drawings (not $y$-monotone) that cannot be straightened out while maintaining the height. We give some applications of our result.