Graph Reconstruction from Path Correlation Data

TL;DR

This paper investigates the conditions under which a directed, weighted communication network graph can be reconstructed solely from boundary measurements of path correlation data, providing necessary and sufficient criteria and an algorithm.

Contribution

It establishes the first comprehensive set of conditions for reconstructing directed graphs from path correlation data and introduces an algorithm for this purpose.

Findings

Derived necessary and sufficient conditions for graph reconstructibility.

Developed an algorithm capable of reconstructing the graph under these conditions.

Analyzed the relationship between reconstructed and true graphs when conditions are not met.

Abstract

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.