Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Separator for $c$-Packed Segments and Curves

Sariel Har-Peled

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.

Separator for $c$-Packed Segments and Curves

Abstract

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

Paper Structure

This paper contains 1 section, 2 theorems, 1 equation.

Table of Contents

  1. Separator for $c$-packed segments

Key Result

Lemma 1.1

Let $S$ be a set of $c$-packed segments in $\mathbb{R}^d$, then for any $p$, and $0 \leq a < b$, we have ${\mathbb{E}}_{x \in [a,b]}\mleft[\#(p,x,S)\mright] \leq \frac{cb}{b-a}$. $\blacktriangleleft$$\blacktriangleleft$

Theorems & Definitions (2)

  • Lemma 1.1
  • Lemma 1.2