Linking disjoint segments into a simple polygon is hard

TL;DR

Determining if disjoint line segments can be connected into a simple polygon by adding segments is computationally hard, specifically NP-hard, highlighting the complexity of this geometric problem.

Contribution

This paper proves that linking disjoint segments into a simple polygon is NP-hard, establishing the computational difficulty of this geometric problem.

Findings

Linking disjoint segments into a simple polygon is NP-hard.

The problem remains hard even when restricted to certain configurations.

This result impacts computational geometry and related algorithms.

Abstract

Deciding whether a family of disjoint 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.