CSE 713 - Expanders: Theory and Applications
- 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
1. Probabilistic Constructions, Existence of Expanders
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
4. Random walks and random walks on expanders, error amplification, derandomization
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
- 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
- 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
7. Expanders, superconcentrators, concentrators, sorting networks and
- N. Alon, Expanders, sorting in rounds and superconcentrators of limited
depth, Proc. 17th ACM Symp. on the Theory of Computing (STOC), Providence,
- 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,
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,
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
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,