## Mathematical Physics and Harmonic Analysis Seminar

**Date:** December 1, 2017

**Time:** 1:50PM - 2:50PM

**Location:** BLOC 628

**Speaker:** Mahmood Ettehad, Texas A&M University

**Title:** *Network graph reconstruction from path correlations (joint with Inverse Problems Seminar)*

**Abstract:** Routing network can be modeled by a connected graph with a set of boundary vertices where the measurements can be taken. Among the possible measurements are the transmission times between any pair of boundary vertices. Furthermore, it has been observed that the correlation between transmission times along two paths can be used as a proxy for the length of the intersection of the paths. The aim is to use this information to solve the problem of network tomography (reconstruct the structure of the entire network together with the length of all links).

Mathematically, given an edge-weighted graph we can measure the weight of the segment common to any two paths A-Z and B-Z, where A, B and Z are boundary vertices. We will present a necessary and sufficient condition for the graph to be reconstructable from this information, and will describe the reconstruction algorithm.

Based on a joint work with Gregory Berkolaiko and Nick Duffield (ECE TAMU).