Fall 2005

- Here is a list of topics and papers suggested for your presentation.
**This list shall be improved and updated considerably.**Again, please feel free to pick your own topic and discuss it with me. - Lastly, the papers listed for a particular topic are, in some cases, not sufficient for a survey on that topic. They are listed as the first starting point.

- N. Alon and Y. Roichman, Random Cayley graphs and expanders, Random Structures and Algorithms 5 (1994), 271-284.

- Noga Alon, Eigenvalues and expanders, Combinatorica 6(2): 83-96 (1986).
- N. Alon, Z. Galil and V. D. Milman, Better expanders and superconcentrators, J. Algorithms 8 (1987), 337-347.
- Joel Friedman, "A proof of Alon's second eigenvalue conjecture and related problems", CoRR cs.DM/0405020: (2004) (A preliminary version appeared in STOC 2003).
- Yonatan Bilu, and Nati Linial, "Lifts,
discrepancy and nearly optimal spectral gaps", To appear in Combinatorica,
(A preliminary version appeared in FOCS 2004).

- N. Alon and M. Capalbo, Explicit unique-neighbor expanders, Proc. of the 43 IEEE FOCS, IEEE (2002), 73-79.
- Omer Reingold, Salil Vadhan, and Avi Wigderson: "Entropy Waves, The Zig-Zag Graph Product, and New Constant-Degree Expanders and Extractors", Annals of Math `02.

- Russell Impagliazzo, David Zuckerman: "How to Recycle Random Bits", FOCS 1989: 248-253.
- Russell Impagliazzo, Noam Nisan, Avi Wigderson: "Pseudorandomness for network algorithms", STOC 1994: 356-364
- Amir Shpilka, Avi Wigderson: "Derandomizing
homomorphism testing in general groups". STOC 2004: 427-435

- D. Song, D. Zuckerman, and J. D. Tygar, Expander Graphs for Digital Stream Authentication and Robust Overlay Networks (IEEE Security and Privacy 2002). [ .ps ]
- Ching Law, Kai-Yeung Siu (MIT), Distributed Construction of Random Expander Networks, INFOCOM 2003.
- C Gkantsidis, M Mihail, A Saberi, Conductance and congestion in power law graphs, SIGMETRICS 2003.
- K Hildrum, R Krauthgamer, J Kubiatowicz, Object Location in Realistic Networks, ACM Symposium on Parallel Algorithms and Architectures 2004.
- C Gkantsidis, M Mihail, A Saberi, GA Atlanta, Random walks in peer-to-peer networks, INFOCOM 2004
- Kirsten Weale Hildrum, Finding near-by objects in P2P Networks, Ph.D. Dissertation, UC Berkeley.
- M Zhong, K Shen, J Seiferas, Non-uniform Random Membership Management in Peer-to-Peer Networks, INFOCOM 2005.
- S Voulgaris, D Gavidia, M van Steen, Inexpensive membership management for unstructured P2P overlays, Journal of Network and Systems Management, 2005

**6. Expanders and coding theory**

- Michael Sipser, Daniel A. Spielman: Expander codes. IEEE Transactions on Information Theory 42(6): 1710-1722 (1996)
- Gilles Zemor: "On Expander Codes", IEEE Transactions on Information Theory 47(2):835-837 (2001).
- Venkatesan Guruswami, Piotr Indyk: "Linear time encodable/decodable codes with near-optimal rate", To appear in IEEE Transactions on Information Theory. (Preliminary Version in STOC'02).
- Venkatesan Guruswami. Error-correcting codes and Expander graphs SIGACT News, 35(3): 25-41, September 2004.
- A. Ta-Shma, D. Zuckerman, and S. Safra, Extractors from Reed-Muller Codes, 2004
- A. Ta-Shma and D. Zuckerman, Extractor codes,

**7. Expanders, superconcentrators, concentrators, sorting networks and
switching networks**

- N. Alon, Expanders, sorting in rounds and superconcentrators of limited depth, Proc. 17th ACM Symp. on the Theory of Computing (STOC), Providence, RI(1985), 98-102.
- N. Alon and P. Pudlak, Superconcentrators of depth 2 and 3; odd levels help (rarely), J. Comp. Sys. Sci. 48 (1994), 194-202.
- Sanjeev Arora, Tom Leighton, and Bruce Maggs, Online Algorithms for Path-selection in a Nonblocking Network, SIAM Journal on Computing, Vol. 25, No. 3, June 1996, pp. 600-625. (Prelim. version in STOC 1990.)
- N. Alon and M. Capalbo, Smaller explicit superconcentrators, Proc. of the Fourteenth Annual ACM-SIAM SODA (2003), 340-346. Also: Internet Mathematics, to appear.
- Ellen Witte Zegura, Evaluating blocking probability in generalized connectors, IEEE/ACM Transactions on Networking (TON), v.3 (1995) n.4, pp. 387--398.
- Jaikumar Radhakrishnan and Amnon Ta-Shma, Bounds dispersers, extractors and depth-two superconcentrators. (FOCS 1997), SIAM Journal on Discrete Mathematics 2000
- R. Shaltiel and C. Umans, Simple Extractors for All Min-Entropies and a New Pseudo-Random Generator,
- Recent Developments in Extractors, Survey article by Ronen Shaltiel
- Any paper on expanders from David
Zuckerman's website.
**I am especially interested in the survey papers there.** - Any paper on expanders, superconcentrators, concentrators from Avi
Wigderson's website
**I am especially interested in explicit construction papers there****.** - Any paper on extractors, superconcentrators from Amnon Ta-shama's website

**8. Expanders, complexity theory, the PCP theorem**

- Noam Nisan: "Pseudorandom generators for space-bounded computation", Combinatorica 12(4): 449-461 (1992).
- Miklos Ajtai, Janos Komlos, Endre Szemeredi, Deterministic Simulation in LOGSPACE, STOC 1987: 132-140.
- Omer Reingold: "Undirected
ST-Connectivity in Logspace", ECCC Tech Report TR04-094, 2004.

Sara Robinson, "Computer Scientist Finds Small-Memory Algorithm for Fundamental Graph Problem", SIAM News, Volume 38, Number 1, January/February 2005. - Irit Dinur, "The PCP Theorem by Gap Amplification", ECCC Technical Report TR05-046, 2005.