Circle graphs can be recognized in linear time

TL;DR

This paper presents a new linear-time algorithm for recognizing circle graphs by utilizing the PC-tree data structure, improving upon previous methods that relied on union-find structures.

Contribution

It introduces a novel linear-time recognition algorithm for circle graphs using PC-trees, eliminating the need for union-find data structures.

Findings

Recognition algorithm runs in linear time

Uses PC-trees instead of union-find structures

First linear-time recognition algorithm for circle graphs

Abstract

To date, the best circle graph recognition algorithm runs in almost linear time as it relies on a split decomposition algorithm that uses the union-find data-structure. We show that in the case of circle graphs, the PC-tree data-structure allows one to avoid the union-find data-structure to compute the split decomposition in linear time. As a consequence, we obtain the first linear-time recognition algorithm for circle graphs.