有界亏格图中子集连通性问题的多项式时间逼近
Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs
摘要：
我们提出了第一多项式时间近似方案（PTASes）的边加权图的有界亏格的子集连通性问题：斯坦纳树，低连通生存网络设计，和子集TSP。该计划运行在O（n log n）的时间嵌入定向和非定向表面上的图。这项工作将Borradaile，Klein和Mathieu的PTAS框架从平面图推广到有界亏格图：任何未来的问题都可以承认平面图的必要结构定理，同样也可以扩展到有界亏格图。
英文摘要：
We present the first polynomial-time approximation schemes (PTASes) for the following subset-connectivity problems in edge-weighted graphs of bounded genus: Steiner tree, low-connectivity survivable-network design, and subset TSP. The schemes run in O(n log n) time for graphs embedded on both orientable and non-orientable surfaces. This work generalizes the PTAS frameworks of Borradaile, Klein, and Mathieu from planar graphs to bounded-genus graphs: any future problems shown to admit the required structure theorem for planar graphs will similarly extend to bounded-genus graphs.
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。
