Complexity results on untangling red-blue matchings

• Published in: Computational geometry : theory and applications Vol. 111; p. 101974
• Main Authors: Das, Arun Kumar, Das, Sandip, da Fonseca, Guilherme D., Gerard, Yan, Rivier, Bastien
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2023; Elsevier
• Subjects: Computer Science; Matching; NP-hard; Planar geometry; Reconfiguration; Matching; NP-hard; Planar geometry; Reconfiguration

Given a matching between n red points and n blue points by line segments in the plane, we consider the problem of obtaining a crossing-free matching through flip operations that replace two crossing segments by two non-crossing ones. We first show that (i) it is NP-hard to α-approximate the shortest...