Separator for $c$-Packed Segments and Curves

2026-04-05

AI Summary

This work proposes a concise and efficient construction algorithm for balanced separators of $c$-packed sets of line segments. By leveraging the geometric properties inherent to $c$-packedness and employing a divide-and-conquer strategy, the method devises a lightweight partitioning procedure that achieves a balanced separator by cutting only $O(c)$ segments. In contrast to prior approaches, this solution not only guarantees an asymptotically optimal number of cuts in theory but also offers a significantly simpler construction and proof. Consequently, it markedly reduces the algorithmic complexity associated with partitioning $c$-packed objects, thereby highlighting both its practical utility and theoretical significance in computational geometry.

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.

Problem

• c-packed
• segments
• balanced separator
• computational geometry

Innovation

• c-packed
• balanced separator
• geometric algorithms
• segment separation