Funding information This article is based uponwork fromCOST Action CA15127 (”Resilient communication services protecting end-user applications from disaster-based failures RECODIS”) supported by COST (European Cooperation in Science and Technology). This work was partially supported by the High Speed Networks Laboratory (HSNLab) at the Budapest University of Technology and Economics, by the BME-Artificial Intelligence FIKP grant of EMMI (BME FIKP-MI/SC), and by the Hungarian Scientific Research Fund (grant No. OTKA FK_17 123957, KH_18 129589, K_17 124171, K_18 128062 and K_17 124171). Several recent works shed light on the vulnerability of networks against regional failures, which are failures ofmultiple pieces of equipment in a geographical region as a result of a natural disaster. To enhance the preparedness of a given network to natural disasters, regional failures and associated Shared Risk Link Groups (SRLGs) should be first identified. For simplicity, most of the previous works assume the network is embedded on an Euclidean plane. Nevertheless, they are on the Earth surface; this assumption causes distortion. In this work, we generalize some of the related results on the plane to the sphere. In particular, we focus on algorithms for listing SRLGs as a result of regional failures of circular or other fixed shape.

中文翻译：

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地球几乎是平的：用于检测平面和球体上网络脆弱区域的精确和近似算法

资金信息 本文基于由 COST（欧洲科技合作组织）支持的 COST Action CA15127（“保护最终用户应用程序免受基于灾难的故障 RECODIS 的弹性通信服务”）的工作。这项工作得到了布达佩斯科技与经济大学高速网络实验室 (HSNLab)、EMMI 的 BME-人工智能 FIKP 赠款 (BME FIKP-MI/SC) 和匈牙利科学研究基金 (授权号 OTKA FK_17 123957、KH_18 129589、K_17 124171、K_18 128062 和 K_17 124171）。最近的几项工作阐明了网络对区域故障的脆弱性，区域故障是自然灾害导致地理区域内多个设备的故障。为了增强特定网络对自然灾害的准备，应首先确定区域故障和相关的共享风险链接组 (SRLG)。为简单起见，之前的大部分工作都假设网络嵌入在欧几里得平面上。尽管如此，它们还是在地球表面；这种假设会导致失真。在这项工作中，我们将平面上的一些相关结果推广到球体。特别是，我们关注由于圆形或其他固定形状的区域故障而列出 SRLG 的算法。我们将平面上的一些相关结果推广到球体。特别是，我们关注由于圆形或其他固定形状的区域故障而列出 SRLG 的算法。我们将平面上的一些相关结果推广到球体。特别是，我们关注由于圆形或其他固定形状的区域故障而列出 SRLG 的算法。