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.

翻译：迄今为止，最优的圆图识别算法运行于近似线性时间，因其依赖于采用并查集数据结构的裂解分解算法。本文证明，对于圆图而言，PC树数据结构可避免使用并查集来计算线性时间的裂解分解。由此，我们首次获得了圆图的线性时间识别算法。