[spectral] graph theory, combinatorics,
coding theory, liar games
Random geometric graphs, probabilistic
methods, algorithm design & analysis
Math 152 Calculus II
Math 230
Intro to Discrete Math
All Teaching
(Project
NExT)
Applied Mathematics
Illinois
Institute of Technology
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1.Linearly bounded liars, adaptive covering codes, and deterministic random walks (arXiv, pdf, slides), J. Comb. 1 (2010), 307-334 (Joel Spencer special issue) (w/Joshua Cooper). Hear Joshua talk about this paper on an episode of Strongly Connected Components (start time 16:04).
2.Variance of the subgraph count for sparse Erdős-Rényi graphs (pdf, slides), Discrete Appl. Math., 158 (2010), 649-658 (w/J.P. Ferry).
3.The spectra of super line multigraphs (pdf), In: B.D. Acharya, G.O.H. Katona, and J. Nesetril, eds., Advances in Discrete Mathematics and Applications: Mysore, 2008 (Proc. Int. Conf. Discrete Math., ICDM-2008, Mysore, India, 2008), pp.81-89. Ramanujan Math. Soc. Lect. Notes Ser., No. 13. Ramanujan Math. Soc., Mysore, India, 2011 (with J. Bagga and D. Ferrero).
4.Two-batch liar games on a general bounded channel (pdf slides), J. Combin. Theory Ser. A 116 (2009), 1253-1270 (w/K. Nyman).
5. Monitoring Schedules for randomly deployed sensor networks, Proceedings of the DIALM-POMC Joint Workshop on Foundations of Mobile Computing (2008), 3-12 (w/G. Calinescu)
6. Random geometric graph diameter in the unit ball, Algorithmica 47 (2007), 421-438 (arXiv pdf) (with J.L. Martin and C.H. Yan). The original publication is available at www.springerlink.com.
Gergely Balint (PhD S`14), Non-adaptive group testing, Steiner systems, and latin squares
James Panek (MS S`17), Graph partitioning with eigenvectors
Melinda Bulin Clardy (MS S`15), Disjunctness properties resulting from concatenation of group testing matrices
Daniel Tietzer (MS F`11) (Thesis: Adaptive covering codes in the q-ary hypercube, thesis errata, corrected thesis )
James Williamson (MS F`11) (Thesis: Analysis of the application of the liar machine to the q-ary pathological liar game with a focus on lower discrepancy bounds)
1.Error-correcting codes, covering codes, and liar games: a unified viewpoint (slides from Menger Day 2008)
2.Diameter, path length, and guidelines for routing in random geometric graphs (using probabilistic methods): see Random geometric graph diameter in the unit ball (arXiv pdf).
3.The Probabilistic Method meets combinatorial coding theory:
Asymmetric binary covering codes (ppt slides) (arXiv), JCTA 100, 2002 (with Joshua Cooper and Andrew B. Kahng).
Improved upper bounds (paper #261) on radius 1 cases by David Applegate, Eric Rains, and Neil Sloane
New upper bounds on code sizes by Geoff Exoo and Esa Seuranen
Improved density upper bound by Michael Krivelevich, Benny Sudakov, and Van Vu
Corresponding density of normal binary covering codes (arXiv) (R.B. Ellis)
4.Torus hitting times and Green's functions (html, images)
5.Hearing the shape of a graph via its spectrum (html, images, wav)
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