English

Notes on Approximation Algorithms for Polynomial-Expansion and Low-Density Graphs

Computational Geometry 2016-03-11 v1

Abstract

This write-up contains some minor results and notes related to our work [HQ15] (some of them already known in the literature). In particular, it shows the following: - We show that a graph with polynomial expansion have sublinear separators. - We show that hereditary sublinear separators imply that a graph have small divisions. - We show a natural condition on a set of segments, such that they have low density. This might be of independent interest in trying to define a realistic input model for a set of segments. Unlike the previous two results, this is new. For context and more details, see the main paper.

Keywords

Cite

@article{arxiv.1603.03098,
  title  = {Notes on Approximation Algorithms for Polynomial-Expansion and Low-Density Graphs},
  author = {Sariel Har-Peled and Kent Quanrud},
  journal= {arXiv preprint arXiv:1603.03098},
  year   = {2016}
}
R2 v1 2026-06-22T13:07:43.014Z