论文标题
在多项式时间内边缘连接性的顶点稀疏
Vertex Sparsification for Edge Connectivity in Polynomial Time
论文作者
论文摘要
顶点稀疏区域中的一个重要开放问题是$（1+ε）$ - 近似剪切的顶点稀疏器，大小接近端子数量。 Chalermsook等人的作品。 （SODA 2021）引入了一种称为Connectivity-$ c $模仿网络的放松，该网络要求构建一个顶点散布器，该sparsifier可在$ k $ terminals之间保持连通性，完全达到$ c $的价值，并向动态连接性数据结构和可生存的网络设计显示了应用程序。我们表明，连接性 - $ c $模仿$ \ widetilde {o}（kc^3）$边缘存在，并且可以在$ n $和$ c $的多项式时间内构造，并且比Chalermsook等人的结果有所改善。 （SODA 2021）对于任何$ c \ ge \ log n $，其运行时的运行时间呈指数为$ c $。
An important open question in the area of vertex sparsification is whether $(1+ε)$-approximate cut-preserving vertex sparsifiers with size close to the number of terminals exist. The work Chalermsook et al. (SODA 2021) introduced a relaxation called connectivity-$c$ mimicking networks, which asks to construct a vertex sparsifier which preserves connectivity among $k$ terminals exactly up to the value of $c$, and showed applications to dynamic connectivity data structures and survivable network design. We show that connectivity-$c$ mimicking networks with $\widetilde{O}(kc^3)$ edges exist and can be constructed in polynomial time in $n$ and $c$, improving over the results of Chalermsook et al. (SODA 2021) for any $c \ge \log n$, whose runtimes depended exponentially on $c$.
