CSE 713 - Random Graphs: Theory and Applications
Fall 2003

• 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. Random Graphs

• W. Aiello, Fan Chung, and L. Lu. Random evolution in massive graphs. In IEEE Symposium on Foundations of Computer Science (FOCS), Las Vegas, NV, October 2001.
• N. Alon, V. Rödl and A. Rucinski, Perfect matchings in $\epsilon$-regular graphs, The Electronic J. Combinatorics 5(1) (1998), R13, 4pp.
• N. Alon, Y. Caro and R. Yuster, Packing and covering dense graphs, J. Combinatorial Designs 6 (1998), 451-472.
• N. Alon, M. Krivelevich and B. Sudakov, List coloring of random and pseudo-random graphs, Combinatorica 19 (1999), 453-472.
• N. Alon, M. Krivelevich and B. Sudakov, Finding a large hidden clique in a random graph, Proc. of the Ninth Annual ACM-SIAM SODA, ACM Press (1998), 594-598. Also: Random Structures and Algorithms 13 (1998), 457-466.

2. Random Graphs & Probabilistic Methods in Networking

• G. Pandurangan, P. Raghavan and E. Upfal. ``Building Low-diameter P2P Networks''. 42nd Annual Symposium on Foundations of Computer Science (FOCS01), pp. 492-499.
• A. Broder, A.M. Frieze , and E. Upfal. ``Static and dynamic path selection on expander graphs: a random walk approach''. Random Structure & Algorithms. Vol. 14, 1999, pp. 87-109
• C. E. Shannon, ``A mathematical theory of communication,'' Bell System Technical Journal, vol. 27, pp. 379-423 and 623-656, July and October, 1948.
• A.Z. Broder, A.M. Frieze, and E. Upfal. ``A general approach to dynamic packet routing with bounded buffers.'' J. Of the ACM, Vol. 48, 2001, pp. 324-349;
• E. Valdimarsson, "Blocking in multirate networks," in Proc. INFO- COM'91, pp. 579-588, 1991.
• Y. Yang and J. Wang, ``On blocking probability of multicast networks,'' IEEE Transactions on Communications, vol. 46, no. 7, July 1998, pp. 957-968.
• Chung, Shun-Ping, Kashper, Arik, Ross, Keith W., "Computing approximate blocking probabilities for large loss networks with state-dependent routing", IEEE/ACM Transactions on Networking, Vol.1, No. 1 (Feb. 1993), pp. 105-115.
• N. Alon, F. R. K. Chung and R. L. Graham, Routing permutations on graphs via matchings, Proc. 25th ACM Symp. on the Theory of Computing (STOC), San Diego, CA, 1993, 583-591. Also: SIAM J. Discrete Math. 7(1994), 513-530.
• I. Stoica, R. Morris, D. Karger, M. Kaashoek, and H. Balakrishnan. Chord: A Scalable Peer-to-Peer Lookup Service for Internet Applications, in Proceedings of ACM SIGCOMM, 2001.
  
• D. Liben-Nowell, H. Balakrishnan, and D. Karger, Analysis of the Evolution of Peer-to-Peer Systems. ACM Conf. on Principles of Distributed Computing (PODC), Monterey, CA, July 2002.
  
• J. Aspnes, Z. Dimadi, and G. Shah. Fault-Tolerant Routing in Peer-to-Peer Systems, Proceedings of the ACM Principles of Distributed Computing (PODC), 2002.
  
• J. Saia, A. Fiat, S. Gribble, A. Karlin, and S. Saroiu. Dynamically Fault-Tolerant Content Addressable Networks, in Proceedings of the 1st International Workshop on Peer-to-Peer Systems (IPTPS'02), March 2002, Cambridge, MA.
  
• S. Ratnasamy, P. Francis, M. Handley, R. Karp, S. Shenker. A Scalable Content-Addressable Network in Proceedings of ACM SIGCOMM, 2001.
  
• Bong-Jun Ko and Dan Rubenstein. A Greedy Approach to Replicated Content Placement Using Graph Coloring Invited Paper SPIE ITCom Conference on Scalability and Traffic Control in IP Networks II, Boston, MA, July 2002.
• R. Kumar, P. Raghavan, S. Rajagopalan, D. Sivakumar, A. Tomkins, and E. Upfal. Stochastic Models for the Web. In Proceedings of the 41st Annual Symposium on the Foundations of Computer Science, 2000.
  
• G. Pandurangan, P. Raghavan, and E. Upfal. Using PageRank to Characterize Web Structure, In Proceedings of the 8th Annual International Computing and Combinatorics Conference (COCOON), LNCS 2387, Springer-Verlag, 330-339, 2002.
  
• W. Aiello, F. Chung-Graham and L.Lu. Random evolution of massive graphs, Handbook on Massive Data Sets, (Eds. James Abello et al.), Kluwer Academic Publishers, (2002), 97-122. Extended abstract appeared in FOCS 2001, 510-519.
  
• A. Barabasi and R. Albert. Emergence of Scaling in Random Networks. Science , 286 (509), 1999.
  
• A. Broder, R. Kumar, F. Maghoul, P. Raghavan, S.Rajagopalan, R. Stata, Andrew Tomkins, J. Weiner.Graph Structure in the Web. In Proceedings of the 9th WWW Conference, 2000.
  
• Alex Fabrikant, Elias Koutsoupias, C.H.Papadimitriou Heuristically Optimized Trade-offs: A new paradigm for the power laws of the Internet, Proc. of STOC 02.
• A. Amis, R. Prakash, T. Vuong, and D.T. Huynh. Max-Min Cluster Formation in Wireless Ad Hoc Networks. In Proc. IEEE INFOCOM, 1999.
  
• P. Gupta and P. Kumar. Critical Power forAsympototic Connectivity in Wireless Networks, in Stochastic Analysis, Control, Optimizationand Applications: A Volume in Honor of W.H.Fleming, W. M. McEneaney, G. Yin, and Q. Zhang(Eds.), Birkhäuser, Boston, 1998.
  
• S.Meguerdichian, F. Koushanfar, M. Potkonjak and M.Srivastava. Coverage problems in wireless ad-hoc sensor networks. Infocom 2001, 1380-1387.
  
• A.Tsirigos, Z.Haas, S.Tabrizi. Multipath routing in mobile adhoc networks or how to route in the presence of topological changes. IEEE MILCOM, 2001.
  

3. Randomized Algorithms

• G. Pandurangan and E. Upfal. ``Can Entropy Characterize Performance of Online Algorithms?'' 12th ACM-SIAM Symposium on Discrete Algorithms, January 2001
• N. Alon, W. F. de la Vega, R. Kannan and M. Karpinski, Random Sampling and Approximation of MAX-CSP Problems, Proc. of the 34 ACM STOC, ACM Press (2002), 232-239.
• David Bruce Wilson, Generating random spanning trees more quickly than the cover time, Proceedings of the twenty-eighth annual ACM symposium on Theory of computing, 296--303, 1996.

4. Small-World Phenomena, Gossip Protocols, and Information Dynamics

• J. Kleinberg. Navigation in a Small World. Nature 406(2000), 845.
• J. Kleinberg. The small-world phenomenon: An algorithmic perspective. Proc. 32nd ACM Symposium on Theory of Computing, 2000. Also appears as Cornell Computer Science Technical Report 99-1776 (October 1999)
• J. Kleinberg. Small-World Phenomena and the Dynamics of Information. Advances in Neural Information Processing Systems (NIPS) 14, 2001.
• D. Kempe, J. Kleinberg, A. Demers. Spatial gossip and resource location protocols. Proc. 33rd ACM Symposium on Theory of Computing, 2001.
• D. Kempe, J. Kleinberg. Protocols and Impossibility Results for Gossip-Based Communication Mechanisms. Proc. 43rd IEEE Symposium on Foundations of Computer Science, 2002.

5. Expanders, Concentrators, Superconcentrators, Generalizers, Extractors

• N. Alon and M. Capalbo, Explicit unique-neighbor expanders, Proc. of the 43 IEEE FOCS, IEEE (2002), 73-79.
• 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, Z. Galil and V. D. Milman, Better expanders and superconcentrators, J. Algorithms 8 (1987), 337-347.
• N. Alon and Y. Roichman, Random Cayley graphs and expanders, Random Structures and Algorithms 5 (1994), 271-284.
• N. Alon and P. Pudlak, Superconcentrators of depth 2 and 3; odd levels help (rarely), J. Comp. Sys. Sci. 48 (1994), 194-202.
• N. Alon and M. Capalbo, Smaller explicit superconcentrators, Proc. of the Fourteenth Annual ACM-SIAM SODA (2003), 340-346. Also: Internet Mathematics, to appear.
• 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

6. Connectors, generalized connectors

• Ellen Witte Zegura, Evaluating blocking probability in generalized connectors, IEEE/ACM Transactions on Networking (TON), v.3 (1995) n.4, pp. 387--398.
• I have hard copies of many papers on this topic. Ask me if you want to present.
  

7. Local Lemma Related

• (****) Beck, József An algorithmic approach to the Lovász local lemma. I. Random Structures Algorithms 2 (1991), no. 4, 343--365.
• Czumaj, Artur; Scheideler, Christian Coloring nonuniform hypergraphs: a new algorithmic approach to the general Lovász local lemma. Proceedings of the Ninth International Conference "Random Structures and Algorithms" (Poznan, 1999). Random Structures Algorithms 17 (2000), no. 3-4, 213--237.