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I've had the pleasure of working with great students.
Most of what I really understand in my field, I learned in working with them.
Graph Embeddings for Low-Stretch Greedy Routing
Andrej's thesis research developed algorithms and heuristics to improve greedy routing – routing in which a packet is forwarded to the neighbor closest to the destination. Andrej's work made heavy use of hyperbolic geometry, and relied on embedding network nodes in the Poincare disk. He showed how to enable growing graphs, embed weighted graphs with low distortion, and achieve greedy routing with low stretch (short paths).
Andrej is currently (2015) Assistant Professor, School of Informatics, European University, Republic of Macedonia.
PhD 2016 coadvised with Evimaria Terzi
Matrix Completion with Structure
Natali's thesis developed new insights into problems involving low-rank matrix completion. While most matrix completion work is statistical in nature, Natali took fundamentally combinatorial approaches, developing an organizing framework and then a new combinatorial algorithm for active matrix-completion. She also developed new methods for identifying low-rank submatrices in a partially-observed matrix.
Natali is currently (2018) Data Scientist at Hush.
On the Dynamics of Interdomain Routing in the Internet
Giovanni's thesis work developed new tools (algorithms and metrics) to analyze the behavior of interdomain routing over time. He developed a data mining approach to detecting large-scale changes in Internet routing that re-occur many times over long timescales, and he showed how to identify the link or Autonomous System (AS) most likely to be reponsible for those events. He also developed new metrics and algorithms for indentifying unusually-routed ASes, and used them to shed light on how global routing patterns have evolved over a thirteen-year period.
Giovanni is currently (2018) Assistant Professor of Computer Science at the Universidade Federal de Viçosa, Brazil.
If you'd like to read more about any of these projects,
all of the papers I have written with my students are available from my publications page.