We present a $9^k\cdot n^{O(1)}$-time algorithm for the proper circular-arc vertex deletion problem, resolving an open problem of van 't Hof and Villanger [Algorithmica 2013] and Crespelle et al. [arXiv:2001.06867]. Our structural study also implies parameterized algorithms for modification problems toward proper Helly circular-arc graphs.

翻译：我们提出了一个9美元k\cdott n ⁇ O(1)}美元时间算法,用于解决适当的圆弧顶部删除问题,解决Van't Hof和Villanger[2013年Algorithmica]和Crespelle et al.[arXiv:2001.06867]和Crespelle et al.[arXiv:2001.06867]这两个未决问题。我们的结构研究还包含参数化算法,用于修改适当的Helly圆弧图的问题。