Efficient Network Analysis: Sparsity, Algorithms, and... Colorings!

School of Mathematics Colloquium
Thursday, September 20, 2018 - 11:00am
1 hour (actually 50 minutes)
Skiles 006
Department of Computer Science, NC State University
Techniques from structural graph theory hold significant promise for designing efficient algorithms for network science. However, their real-world application has been hampered by the challenges of unrealistic structural assumptions, hidden costs in big-O notation, and non-constructive proofs. In this talk, I will survey recent results which address many of these concerns through an algorithmic pipeline for structurally sparse networks, highlighting the crucial role of certain graph colorings, along with several open problems. For example, we give empirical and model-based evidence that real-world networks exhibit a form of structural sparsity known as "bounded expansion,'' and discuss properties of several low-treedepth colorings used in efficient algorithms for this class. Based on joint works with E. Demaine, J. Kun, M. O'Brien, M. Pilipczuk, F. Reidl, P. Rossmanith, F. Sanchez Villaamil, and S. Sikdar.