Research Interests  

[spectral] graph theory, combinatorics,

    coding theory, liar games
Random geometric graphs, probabilistic

    methods, algorithm design & analysis

Fall `09 Teaching

Math 557-01
IPRO 321
All Teaching (Project NExT)

Curriculum Vitae
(pdf html)

Applied Mathematics
Illinois Institute of Technology
10 W. 32nd Street

E1 Bldg., Rm. 208

Chicago, IL 60616

Office: E1 105C
Ph.: (312) 567-5336

Selected Research Papers (complete listing)

1. Linearly bounded liars, adaptive covering codes, and deterministic random walks (arXiv, pdf, slides) submitted (w/Joshua Cooper).

2. Variance of the subgraph count for Erdős-Rényi graphs (pdf, slides), Disc. Appl. Math., doi:10.1016/j.dam.2009.11.012 (w/J.P. Ferry).

3. Two-batch liar games on a general bounded channel (pdf slides), J. Combin. Theory Ser. A 116 (2009), 1253-1270 (w/K. Nyman).

4.  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)

5.  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.

5. Asymmetric binary covering codes (arXiv pdf), J. Combin. Theory Ser. A 100 (2002), 232-249 (2002) (w/J.N. Cooper, A.B. Kahng).

Samples of Research Interests

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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