Counterexample for the 2-approximation of finding partitions of rectilinear polygons with minimum stabbing number

TL;DR

This paper provides a counterexample demonstrating that the previously proposed 2-approximation algorithm for partitioning rectilinear polygons with minimal stabbing number does not always produce near-optimal solutions.

Contribution

The paper identifies a flaw in the existing approximation algorithm by Durocher and Mehrabi, showing it can fail to achieve the claimed approximation ratio.

Findings

Counterexample disproves the 2-approximation guarantee

Highlights limitations of current approximation algorithms

Suggests need for improved methods

Abstract

This paper presents a counterexample for the approximation algorithm proposed by Durocher and Mehrabi [1] for the general problem of finding a rectangular partition of a rectilinear polygon with minimum stabbing number.