Linking disjoint axis-parallel segments into a simple polygon is hard too

TL;DR

The paper proves that determining whether disjoint axis-parallel segments can be connected into a simple polygon is an NP-hard problem, highlighting computational complexity challenges in geometric graph construction.

Contribution

It establishes the NP-hardness of linking disjoint axis-parallel segments into a simple polygon, a previously unresolved complexity question in computational geometry.

Findings

NP-hardness of linking disjoint axis-parallel segments into a simple polygon

Complexity result impacts geometric graph construction algorithms

Highlights computational difficulty in related geometric problems

Abstract

Deciding whether a family of disjoint axis-parallel line segments in the plane can be linked into a simple polygon (or a simple polygonal chain) by adding segments between their endpoints is NP-hard.