CSE 713 - Expanders: Theory and Applications
Fall 2005
History/Overview/Survey Articles
- N. Alon, Algebraic and probabilistic methods
in Discrete Mathematics, in: "Visions in Mathematics, Towards 2000",
(N. Alon et. al. eds.), Birkhäuser, 2000, pp. 455-470.
- N. Alon, Spectral techniques in graph
algorithms, Lecture Notes in Computer Science 1380 (C. L. Lucchesi and
A. V. Moura, Eds.), Sringer, Berlin, 1998, 206-215.
- N. Alon, Randomness and pseudo-randomness
in Discrete Mathematics, Proc. of the 2 European Congress of Mathematics,
Progress in Mathematics 168 (1998), 1-14.
- Noam Nisan and Amnon Ta-Shma. Extracting
Randomness: A Survey and New Constructions. JCSS 1999
- Amnon Ta-Shma's Dissertation, Refining
Randomness Hebrew University 1996
- Peter G. Doyle and J. Laurie Snell Random
Walks and Electric Networks. A probably more up-to-date version is here
- David Xiao, "The
Evolution of Expander Graphs", AB Thesis, Harvard University, 2003.
- Nati Linial, "Expanders,
eigenvalues and all that", Invited Talk, NIPS, Dec 2004.
- Sara Robinson, "Computer
Scientist Finds Small-Memory Algorithm for Fundamental Graph Problem",
SIAM News, Volume 38, Number 1, January/February 2005.
- L. Lovász: Random
Walks on Graphs: A Survey [in: Combinatorics, Paul Erdõs is Eighty,
Vol. 2 (ed. D. Miklós, V. T. Sós, T. Szõnyi), János
Bolyai Mathematical Society, Budapest, 1996, 353--398.]
- Peter Sarnak, What
is an expander, Notices of the AMS, Vol 51 (7), 2004.
- Mark Jerrum's page
has many related links.
Related classes and notes
- CS369E:
Expanders in Computer Science (Spring 2005), a class taught at UChicago
taught by Cynthia Dwork
and Prahladh Harsha.
- Michael
Nielsen's notes on expanders (2005)
- CS 225:
Pseudorandomness (Spring 2004), a course by Salil P. Vadhan
- Randomized
Algorithms (2004), a course by Dana
Randall
- 15-859(M):
Randomized Algorithms (2004), a course by Anupam
Gupta and Shuchi Chawla
- Amnon
Ta-shma's expanders class (2003)
- CMSC858T Randomized
Algorithms (Spring 2003), a course by Aravind
Srinivasan
- CS 174 Randomized Algorithms
(Spring 2003), a course by Luca
Trevisan.
- CSE
590VG: Codes and Pseudorandom Objects (Winter 2003), a course by Venkatesan
Guruswami
- Randomized
Algorithms (Fall 2003), a course by John
H. Reif
- Course 67659:
Expander graphs and their applications (Spring 2002), a course by Nati
Linial and Avi Wigderson
- Essential Coding Theory
(2002), a course by Madhu Sudan.
- Randomized
Methods in Computation (2001), a course by Oded
Goldreich
- Randomized
Algorithms (1997), a course by Avrim Blum.
Representative books on Random Graphs, Probability Theory, Coding Theory,
Switching Networks, Expanders, Algebraic Graph Theory
- Doyle and Snell, Random
Walks on Electronic Networks, MAA, 1984. [Now available for free.]
- Bella Bolobas, Random Graphs (2nd ed.), Cambridge University
Press, Studies in Advanced Mathematics, #73, September 2001.
- Alon, Noga; Spencer, Joel H. The probabilistic
method. Second edition. Wiley-Interscience Series in Discrete
Mathematics and Optimization. John Wiley & Sons, New York, 2000. xviii+301
pp. ISBN: 0-471-37046-0
- Molloy, Michael; Reed, Bruce Graph colouring and the probabilistic
method. Algorithms and Combinatorics, 23. Springer-Verlag, Berlin,
2002. xiv+326 pp. ISBN: 3-540-42139-4
- Kallenberg, O. Foundations of Modern Probability. New York:
Springer-Verlag, 1997.
- Rajeev Motwani, Prabhakar Raghavan, Randomized Algorithms,
Cambridge University Press, June 1995.
- F.J. MacWilliams and N.J.A. Sloane, The Theory of Error Correcting Codes,
North-Holland, Amsterdam, 1981.
- J. H. van Lint, Introduction to Coding Theory, Springer Verlag, Berlin,
1999.
- Chris Godsil, Gordon Royle, Algebraic graph theory, Springer; 1 edition
(April 20, 2001)
- Norman Biggs, Algebraic Graph Theory, Cambridge University Press;
2 edition (February 3, 1994)
- Fan Chung, Spectral Graph Theory (CBMS Regional Conference Series
in Mathematics, No. 92), American Mathematical Society (May 1, 1997)
- Dragos M. Cvetkovic, Michael Doob, Horst Sachs, Spectra of Graphs,
Academic Press; 3rd Revised edition (August 1, 1997)
- Joseph Y. Hui, Switching and Traffic Theory for Integrated Broadband
Networks, Kluwer Academic Publishers / January 1990
- Frank Hwang, The Mathematical Theory of Nonblocking Switching Networks,
World Scientific Publishing Company, 2004
- Ding-Zhu Du and Hung Q. Ngo (editors), Advances in Switching Networks,
Network Theory and Applications Series, Vol. 5, Kluwer Academic Publisher
(June 2001), 368pp., ISBN 0-7923-6953-X
Some free books