CSE 713 - Expanders: Theory and Applications
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.

1. Probabilistic Constructions, Existence of Expanders

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

2. Expanders and eigenvalues

• 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).
  

3. Explicit constructions

• 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.

4. Random walks and random walks on expanders, error amplification, derandomization

• 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
  

5. Expanders and P2P/Overlay Networks

• 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.