再谈典型序列--图的宽度参数计算
Typical Sequences Revisited --- Computing Width Parameters of Graphs
摘要：
在这项工作中，我们给出了一个结构引理合并的典型序列，这是在1991年引入的概念[Lagergren和Arnborg，Bodlaender和Kloks，都ICALP 1991]，以获得建设性的线性时间参数化算法的树宽和路径宽度。引理解决了这些算法的运行时瓶颈，但到目前为止，它并没有导致渐近更快的算法。然而，我们应用引理表明，割宽和修改割宽的串联平行有向图可以在$\mathcal{O}(n^2)$时间计算。
英文摘要：
In this work, we give a structural lemma on merges of typical sequences, a notion that was introduced in 1991 [Lagergren and Arnborg, Bodlaender and Kloks, both ICALP 1991] to obtain constructive linear time parameterized algorithms for treewidth and pathwidth. The lemma addresses a runtime bottleneck in those algorithms but so far it does not lead to asymptotically faster algorithms. However, we apply the lemma to show that the cutwidth and the modified cutwidth of series parallel digraphs can be computed in $\mathcal{O}(n^2)$ time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
