Separator for $c$-Packed Segments and Curves

TL;DR

The paper presents a simplified algorithm for finding balanced separators in $c$-packed segments, which cuts only $O(c)$ segments, improving understanding of such geometric structures.

Contribution

It offers a simpler proof for a known separator algorithm for $c$-packed segments, enhancing clarity and accessibility.

Findings

Separator cuts only $O(c)$ segments

The proof of the separator's properties is simpler than previous ones

The algorithm is effective for $c$-packed segments

Abstract

We provide a simple algorithm for computing a balanced separator for a set of segments that is $c$-packed, showing that the separator cuts only $O(c)$ segments. While the result was known before, arguably our proof is simpler.