具有凹费用的虚拟专用网设计问题（Oberwolfach摘要）
The Virtual Private Network Design Problem with Concave Costs (Oberwolfach abstract)
摘要：
对称虚拟专用网设计（VPND）问题涉及在通信网络中的链路（边缘）上购买容量，使得可以满足某些业务需求。我们调查的自然概括VPND的每单位容量的成本可能会降低，如果大量的容量被保留（规模经济原则）。容量成本的增长由非递减凹函数$f$建模。我们称这个问题为凹对称虚拟专用网设计（cVPND）问题。在证明了所谓的金字塔路由问题的泛化以及cVPND具有所谓的树路由属性之后，我们研究了cVPND的近似算法。对于一般的$f$，利用Grandoni和Italiano关于所谓的单源批量购买问题的已知结果，我们给出了一个随机的24.92-近似算法.
英文摘要：
The symmetric Virtual Private Network Design (VPND) problem is concerned with buying capacity on links (edges) in a communication network such that certain traffic demands can be met. We investigate a natural generalization of VPND where the cost per unit of capacity may decrease if a larger amount of capacity is reserved (economies of scale principle). The growth of the cost of capacity is modelled by a non-decreasing concave function $f$. We call the problem the concave symmetric Virtual Private Network Design (cVPND) problem. After showing that a generalization of the so-called Pyramidal Routing problem and hence also the cVPND have the so-called tree routing property, we study approximation algorithms for cVPND. For general $f$, using known results on the so-called Single Source Buy at Bulk problem by Grandoni and Italiano, we give a randomized 24.92-approximation algorithm.
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。
