基于路径相关数据的图形重构
Graph Reconstruction from Path Correlation Data
摘要：
通信网络可以被建模为具有边权重的有向连通图，边权重表征诸如损耗和延迟的性能度量。网络断层扫描的目的是推断这些边的权重，从他们的路径版本上测量的一组相交的路径之间的边界顶点的子集，甚至底层图时，这是未知的。特别地，路径度量之间的时间相关性已经被用来推断由路径交叉点形成的子路径上的复合权重。我们将这些子路径权重称为路径相关数据。在本文中，我们问以下问题：当可以恢复的基础加权图只知道边界顶点和路径相关数据？我们建立充要条件的一个图是从这些信息重建，并描述了一个算法来执行重建。根据我们的条件，结果适用于有向图与非对称边权重，并容纳路径所产生的非对称路由在底层通信网络。我们还描述了我们的算法产生的图之间的关系和真正的图的情况下，我们的条件不满足。
英文摘要：
A communication network can be modeled as a directed connected graph with edge weights that characterize performance metrics such as loss and delay. Network tomography aims to infer these edge weights from their pathwise versions measured on a set of intersecting paths between a subset of boundary vertices, and even the underlying graph when this is not known. In particular, temporal correlations between path metrics have been used infer composite weights on the subpath formed by the path intersection. We call these subpath weights the Path Correlation Data. In this paper we ask the following question: when can the underlying weighted graph be recovered knowing only the boundary vertices and the Path Correlation Data? We establish necessary and sufficient conditions for a graph to be reconstructible from this information, and describe an algorithm to perform the reconstruction. Subject to our conditions, the result applies to directed graphs with asymmetric edge weights, and accommodates paths arising from asymmetric routing in the underlying communication network. We also describe the relationship between the graph produced by our algorithm and the true graph in the case that our conditions are not satisfied.
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