A Survey and a New Competitive Method for the Planar min-# Problem

TL;DR

This paper surveys various approximation algorithms for the planar min-# problem, highlighting their strengths and weaknesses, and introduces a new competitive method to improve solution quality.

Contribution

It provides a comprehensive survey of existing algorithms and proposes a novel competitive approach for the planar min-# problem.

Findings

Most algorithms have trade-offs between approximation quality and computational complexity.

The new method outperforms existing algorithms in certain benchmarks.

The survey identifies gaps and future directions in the field.

Abstract

We survey most of the different types of approximation algorithms which minimize the number of output vertices. We present their main qualities and their inherent drawbacks.