


Lecture 1 (9/29/2005)
Summary: Discussed examples of social networks, common properties of social networks (power law degree distribution, small world phenomenon, and high clustering coefficient), and the structure of the web graph.
Recommended reading: · Broder, R. Kumar, F. Maghoul, P. Raghavan, S. Rajagopalan, R. Stata, A. Tomkins, J. Wiener. Graph structure in the web, 9th International World Wide Web Conference, May 2000.
Other references: · M. Faloutsos, P. Faloutsos and C. Faloutsos. On powerlaw relationships of the Internet topology, ACM SIGCOMM 1999. · J. Kleinberg, and S. Lawrence. The structure of the Web, Science 294, 18491850, November 2001. · A. Barabasi. Network Theory  The Emergence of the Creative Enterprise, Science 308, 639641, 2005. · S. Milgram. The small world problem. Psychology Today 1, 6167, 1967. · J. Travers, and S. Milgram. An experimental study of the small world problem, Sociometry 32, 425443, 1969. · S. H. Strogatz. Exploring complex networks, Nature 410, 268276, March 2001. · R. Albert, H. Jeong, A. Barabasi. Diameter of the World Wide Web, Nature 401, 130131, 1999.
Lecture 2 (10/4/2005)
Summary: Discussed several generative models for power law distributions. Defined ErdosRenyi graphs and preferential attachment graphs, and gave a heuristic argument for computing the degree distribution of preferential attachment graphs.
Recommended reading: · M. Mitzenmacher. A brief history of generative models for power law and lognormal distributions. Internet Mathematics 1, No 2, 226251, 2005. · X. Gabaix. Zipf’s law for cities: an explanation, Quarterly Journal of Economics 114, 739767, 1999.
Other references: · Barabasi, and R. Albert. Emergence of scaling in random networks, Science 286, 509512. 1999. · B. Bollobas, O. Riordan, J. Spencer, G. Tusnady. The degree sequence of a scalefree random graph, Random Structures and Algorithms 18, 279290, 2001. · B. Conrad, and M. Mitzenmacher. Power laws for monkeys typing randomly: the case of unequal probabilities, IEEE Trans on Information Theory 50, No 7, July 2004. · W. Aiello, F. Chung, and L. Lu. A random graph model for massive graphs, In proceedings of STOC 2000.
Lecture 3 (10/6/2005)
Summary: Sketched the analysis of the degree distribution of preferential attachment graphs. Defined the copying model and the Heuristically Optimized Tradeoffs model. Started the discussion on the smallworld networks.
Recommended reading: · B. Bollobas, O. Riordan, J. Spencer, G. Tusnady. The degree sequence of a scalefree random graph, Random Structures and Algorithms 18, 279290, 2001. · D.J. Watts, and S.H. Strogatz. Collective dynamics of smallworld networks, Nature 393, 440442, 1998
Other references: · R. Kumar, P. Raghavan, S. Rajagopalan, D. Sivakumar, A. Tomkins, and E. Upfal. Stochastic models for the web graph, In proceedings of FOCS 2000. · A. Fabrikant, E. Koutsoupias, C. H.Papadimitriou. Heuristically Optimized Tradeoffs, In proceedings of STOC 2002. · B. Bollobas, C. Borgs, J. Chayes, and O. Riordan. Directed scalefree graphs, Proceedings of the 14th ACMSIAM Symposium on Discrete Algorithms, 132139, 2003. · J. Carlson, and J. Doyle. Highly optimized tolerance: a mechanism for power laws in designed systems, Physics Review E 60(2), 14121427, 1999. · B. Bollobas and F.R.K. Chung. The diameter of a cycle plus a random matching, SIAM J. Discr. Math. 1, 328333, 1988.
Lecture 4 (10/11/2005)
Summary: Discussed decentralized search in smallworld networks. Gave an intuition and proof as to why strangers are able to find short paths between each other in a social network (as in Milgram’s experiment).
Recommended reading: · J. Kleinberg. The SmallWorld Phenomenon: An Algorithmic Perspective, Proceedings of the 32^{nd} ACM Symposium on Theory of Computing (STOC), 2000.
Other references: · J. Kleinberg. SmallWorld Phenomena and the Dynamics of Information. Advances in Neural Information Processing Systems (NIPS) 14, 2001. · G.S. Manku, M. Naor, and U. Wieder. Know thy Neighbor’s Neighbor: the Power of Lookahead in Randomized P2P Networks, Proceedings of the 36^{th} ACM Symposium on Theory of Computing (STOC), 2004. · C. Martel and V. Nguyen. Analyzing Kleinberg's (and Other) SmallWorld Models, Proceedings of 23^{rd} ACM Symposium on Principles of Distributed Computing (PODC), 2004.
Lecture 5 (10/13/2005)
Summary: Concluded the topic of smallworld networks with a discussion of the paper of LibenNowell et al. (on a generalization of Kleinberg’s model), and the paper of Robsenblat and Mobius (on the fragmentation of social networks as a consequence of lower communication costs). Introduced some basic concepts in game theory and presented a few gametheoretic models of network formation, in particular the noncooperative models of BalaGoyal and Fabrikant et al. and the cooperative model of Jackson and Wolinsky.
Recommended reading: · M.R. Henzinger. Algorithmic Challenges in Web Search Engines, Internet Mathematics 1, 115123, 2003. · V. Bala and S. Goyal. A Noncooperative Model of Network Formation, Econometrica 68, 11811229, 2000. · M.O. Jackson and A. Wolinsky. A Strategic Model of Social and Economic Networks, Journal of Economic Theory 71, 4474, 1996.
Other references: · D. LibenNowell, J. Novak, R. Kumar, P. Raghavan, and A. Tomkins. Geographic Routing in Social Networks, In Proceedings of the National Academy of Sciences (PNAS) 102, 1162311628, 2005. · M. Mobius and T. Rosenblat. Getting Closer or Drifting Apart, Quarterly Journal of Economics 119, 9711009, 2004. · M.O. Jackson. The Economics of Social Networks, to appear in the Proceedings of the 9th World Congress of the Econometric Society, R. Blundell, W. Newey, and T. Persson, editors, Cambridge University Press. (a survey of social networks and generative models) · M.O. Jackson, A Survey of Models of Network Formation: Stability and Efficiency, Chapter 1 in Group Formation in Economics; Networks, Clubs and Coalitions, G. Demange and M. Wooders, editors, Cambridge University Press, 2004. (a survey of network formation games in the economics literature) · B. Dutta and M.O. Jackson. On the Formation of Networks and Groups, Introduction in Models of the Strategic Formation of Networks and Groups, B. Dutta and M.O. Jackson, editors, Springer, 2003. (a short description of some papers on network formation games in the economics literature) · A. Falk and M. Kosfeld. It’s all about Connections: Evidence on Network Formation, CEPR Discussion Paper no. 3970, London, Centre for Economic Policy Research, 2003. (an experiment with the BalaGoyal model) · A. Fabrikant, A. Luthra, E. Maneva, C.H. Papadimitriou, and S. Shenker. On a Network Creation Game, Proceedings of the 22^{nd} ACM Symposium on Principles of Distributed Computing (PODC), 2003. · E. Anshelevich, A. Dasgupta, E. Tardos, and T. Wexler. NearOptimal Network Design with Selfish Agents, Proceedings of the 35^{th} ACM Symposium on Theory of Computing (STOC), 2003.
Lecture 6 (10/18/2005)
Summary: Discussed HITS (hubs and authorties) and PageRank algorithms for ranking web pages using link analysis.
Recommended reading: · J. Kleinberg. Authoritative sources in a hyperlinked environment. Journal of the ACM 46, 1999. · S. Brin and L. Page. The Anatomy of a LargeScale Hypertextual Web Search Engine. Proc. 7th International World Wide Web Conference, 1998.
Other references: · L. Page, S. Brin, R. Motwani, and T. Winograd. The PageRank citation ranking: bringing order to the web. Stanford CS tech report SIDLWP19990120. · A. Borodin, J. S. Rosenthal, G. O. Roberts, P. Tsaparas, Finding Authorities and Hubs From Link Structures on the World Wide Web. 10th International World Wide Web Conference, May 2001.
Lecture 7 (10/20/2005)
Summary: Discussed the paper of Zhang et al. on the collusion problem for PageRank, and the paper of Altman and Tennenholtz on an axiomatic approach to define PageRank.
Recommended reading: · Hui Zhang, Ashish Goel, Ramesh Govindan, Kahn Mason, Benjamin Van Roy. Making EigenvectorBased Reputation Systems Robust to Collusion. Algorithms and Models for the WebGraph: Third International Workshop, (WAW 2004), 92104, 2004. · A. Altman and M. Tennenholtz. Ranking Systems: The PageRank Axioms, ACM Conference on Electronic Commerce, 18, 2005.
Other references: · K. Arrow. A Difficulty in the Concept of Social Welfare, Journal of Political Economy 58, 328346, 1950. · J. Sethuraman, C.P. Teo, and R. Vohra. Integer Programming and Arrovian Social Welfare Functions, Mathematics of Operations Research 28, 309326, 2003.
Lecture 8 (10/25/2005)
Guest Lecturer: Kamal Jain
Lecture 9 (10/27/2005)
Summary: Started the topic of finding communities and clustering based on the link structure. Discussed two network flow based algorithms for finding communities, and defined the problem of correlation clustering.
Recommended reading: · M. Charikar, Greedy Approximation Algorithms for Finding Dense Components in Graphs, in proceedings of APPROX 2000. · G.W. Flake, S. Lawrence, and C.L. Giles. Efficient identification of web communities. Proc. of the 6th International Conference on Knowledge Discovery and Data Mining (KDD), 2000.
Other references: · G. Flake, S. Lawrence, C. L. Giles, and F. Coetzee. Selforganization and identification of web communities. IEEE Computer, 35:3, March 2002. · G. Flake, K. Tsioutsiouliklis, and R.E. Tarjan. Graph clustering and minimum cut trees. Internet Mathematics 1, No. 4, 385408.
Lecture 10 (11/1/2005)
Summary: Presented an O(log n) linearprogramming based approximation algorithm for minimizing disagreements in the correlation clustering problem with general edge weights. Defined another clustering problem called the metric labeling problem which has applications in web page clustering as well as image processing (see Nov. 8^{th} lecture for references).
Recommended reading: · N. Bansal, A. Blum, and S. Chawla. Correlation Clustering, Machine Learning 56, 89113, 2004. · M. Charikar, V. Guruswami, and A. Wirth. Clustering with qualitative information, IEEE Symposium on Foundations of Computer Science, 52433, 2003. · J. Kleinberg and E. Tardos. Approximation Algorithms for Classification Problems with Pairwise Relationships: Metric Labeling and Markov Random Fields, IEEE Symposium on Foundations of Computer Science, 1423, 1999.
Other references: · E. Demaine and N. Immorlica, Correlation Clustering with Partial Information, Approximation Algorithms for Combinatorial Optimization Problems, 113, 2003. · D. Emanuel and A. Fiat. Correlation Clustering – Minimizing Disagreements on Arbitrary Weighted Graphs, European Symposium on Algorithms, 208220, 2003. · C. Swamy. Correlation Clustering: Maximizing Agreements via Semidefinite Programming, ACMSIAM Symposium on Discrete Algorithms, 519520, 2004. · M. Charikar and A. Wirth. Maximizing quadratic progams: extending Grothendieck's inequality, IEEE Symposium on Foundations of Computer Science, 5460, 2004. · I. Giotis and V. Guruswami. Correlation Clustering with a fixed number of clusters, ACMSIAM Symposium on Discrete Algorithms, to appear, 2006.
NO LECTURE ON 11/3/2005
Lecture 11 (11/8/2005)
Summary: Presented a linearprogramming based 2approximation algorithm for the metric labeling problem under a uniform metric. Discussed spectral clustering algorithms.
Recommended reading: · J. Kleinberg and E. Tardos. Approximation Algorithms for Classification Problems with Pairwise Relationships: Metric Labeling and Markov Random Fields, IEEE Symposium on Foundations of Computer Science, 1423, 1999. · Lecture notes of Dan Spielman’s course at Yale (in particular, Lecture 4). · D. Spielman, S.H. Teng, Spectral Partitioning Works: Planar graphs and finite element meshes, Proceedings of the 37th Annual IEEE Conference on Foundations of Computer Science, 1996.
Other references: · A. Gupta and E. Tardos. A Constant Factor Approximation Algorithm for a Class of Classification Problems, ACM Symposium on the Theory of Computing, 652658, 2000. · C. Chekuri, S. Khanna, J. Naor, and L. Zosin. A Linear Programming Formulation and Approximation Algorithms for the Metric Labeling Problem. SIAM J. Discrete Math 18, 608625, 2004. · J. Naor and R. Schwartz. Balanced metric labeling, ACM Symposium on Theory of Computing, 582591, 2005.
Lecture 12 (11/10/2005)
Summary: Proved Cheeger’s inequality and concluded the discussion of spectral clustering algorithms. Discussed peering relations on the Internet, and the stability of BGP protocol.
Recommended reading: · Lecture notes of Dan Spielman’s course at MIT. · D. Spielman, S.H. Teng, Spectral Partitioning Works: Planar graphs and finite element meshes, Proceedings of the 37th Annual IEEE Conference on Foundations of Computer Science, 1996. · L. Gao and J. Rexford, Stable Internet routing without global coordination, IEEE/ACM Transactions on Networking, pp. 681692, December 2001.
Other references: · Course material of Jennifer Rexford’s course on Internet Routing.
NO LECTURE ON 11/15/2005
Lecture 13 (11/17/2005)
Summary: Defined the rank aggregation problem, and discussed the axiomatic approach (Arrow’s impossibility result) as well as the optimization approach ( Kendall and Footrule distances, Kemeny aggregation). Presented and analyzed the algorithm of Ailon, Charikar, and Newman for rank aggregation.
Recommended reading: · C. Dwork, R. Kumar, M. Naor, D. Sivakumar. Rank aggregation methods for the Web. 10th International World Wide Web Conference, May 2001. · N. Ailon, M. Charikar, and A. Newman, Aggregating Inconsistent Information: Ranking and Clustering, Proceedings of the 37th ACM Symposium on Theory of Computing, 2005.
Other references: · R. Fagin, R. Kumar, and D. Sivakumar. Comparing top k lists, SIAM J. Discrete Mathematics 17, no. 1, pp. 134160, 2003. · R. Fagin, R. Kumar, and D. Sivakumar, Efficient similarity search and classification via rank aggregation. Proc. ACM SIGMOD Conference (SIGMOD '03), pp. 301312, 2003. · R. Fagin, R. Kumar, M. Mahdian, D. Sivakumar, and E. Vee, Comparing and aggregating rankings with ties. Proc. ACM Symposium on Principles of Database Systems (PODS '04), pp. 4758, 2004.
Lecture 14 (11/22/2005)
Summary: Discussed the role of reputation mechanisms in electronic marketplaces, and challenges in designing such systems. Presented the gametheoretic model of Dellarocas, and a sketch of its analysis.
Recommended reading: · P. Resnick, R. Zeckhauser, E. Friedman, and K. Kuwabara, Reputation Systems, Communications of the ACM 43, No. 12, 4548, December 2000. · C. Dellarocas, Efficiency and Robustness of Binary Feedback Mechanisms in Trading Environments with Moral Hazard, MIT Sloan School of Management working paper No. 429703, 2003.
Other references: · P. Resnick, R. Zeckhauser, J. Swanson, K. Lockwood, The value of reputation on Ebay: A controlled experiment, KSG Working Paper No. RWP03007, July 2002. · C. Dellarocas, Analyzing the economic efficiency of eBaylike online reputation reporting mechanisms. Proceedings of the 3rd ACM Conference on Electronic Commerce, Tampa, FL, October 1416, 2001. · R. Jurca and B. Faltings. Eliciting Truthful Feedback for Binary Reputation Mechanisms. Proceedings of the International Conference on Web Intelligence, 2004.
NO LECTURE ON 11/24/2005 (THANKSGIVING)
Lecture 15 (11/29/2005)
Summary: Reviewed peertopeer (P2P) networks including Napster, Gnutella, and Chord. Discussed search and content storage for each of these systems as well as the dynamics of Chord.
Recommended reading: · S. AndroutsellisTheotokis and D. Spinellis, A Survey of PeertoPeer Content Distribution Technologies, ACM Computing Surveys (CSUR), pp. 335371, December 2004. · Xiuqi Li and Jie Wu, Searching Techniques in PeertoPeer Networks. · CHORD: I. Stoica, R. Morris, D. LibenNowell, D.R. Karger, M.F. Kaashoek, F. Dabek, and H. Balakrishnan, Chord: A Scalable Peertopeer Lookup Protocol for Internet Applications, Proceedings of the ACM SIGCOMM Conference, 2001. · D. LibenNowell, H. Balakrishnan, D. Karger, Analysis of the Evolution of PeertoPeer Systems, Proceedings of PODC, 2002.
Other references: · CAN: S. Ratnasamy, P. Francis, M. Handley, R. Karp, S. Shenker, A Scalable ContentAddressable Network, Proceedings of the ACM SIGCOMM Conference, 2001. · GNUTELLA: The Gnutella Protocol Specification version 0.41 · GIA: Y. Chawathe, S. Ratnasamy, L. Breslau, N. Lanham, S. Shenker, Making Gnutellalike P2P Systems Scalable, Proceedings of the ACM SIGCOMM Conference, 2003. · G. Pandurangan, P. Raghavany, E. Upfal, Building LowDiameter P2P Networks, Proceedings of the IEEE Conference on the Foundations of Computer Science (FOCS), 2001. · C. Gkantsidis, M. Mihail, and A. Saberi, Random Walks in PeertoPeer Networks, INFOCOM, 2004. · C. Gkantsidis, M. Mihail, and A. Saberi, Hybrid Search Schemes for Unstructured PeertoPeer Networks, INFOCOM, 2005.
Lecture 16 (12/1/2005)
Summary: Discussed recommendation systems such as those used by Amazon to suggest books to prospective buyers. Analyzed four systems with varying assumptions/requirements regarding the preferences of the user population.
Recommended reading: · R. Kumar, P. Raghavan, S. Rajagopalam, and A. Tomkins, Recommendation Systems: A Probabilistic Analysis, Proceedings of the IEEE Conference on Foundations of Computer Science (FOCS), 1998. · J. Kleinberg and M. Sandler, Convergent Algorithms for Collaborative Filtering, Proceedings of the ACM Conference on Electronic Commerce (EC), 2003. · P. Drineas, I. Kerenidis, P. Raghavan, Competitive Recommendation Systems, Proceedings of ACM Symposium on Theory of Computing (STOC), 2002. · B. Awerbuch, B. PattShamir, D. Peleg, and M. Tuttle, Improved Recommendation Systems, Proceedings of the ACMSIAM Symposium on Discrete Algorithms, 2005.
Other references: · Y. Azar, A. Fiat, A.R. Karlin, F. McSherry, and J. Saia, Spectral Analysis of Data, Proceedings of the ACM Symposium on Theory of Computing (STOC), 2001. · B. Awerbuch and R. Kleinberg, Competitive Collaborative Learning, Proceedings of the 18th Annual Conference on Learning Theory (COLT), 2005. · J. Kleinberg and M. Sandler, Using Mixture Models for Collaborative Filtering, Proceedings of the ACM Symposium on Theory of Computing (STOC), 2004. · P. Drineas, A. Frieze, R. Kannan, S. Vempala, and V. Vinay, Clustering Large Graphs via the Singular Value Decomposition, Proceedings of the ACMSIAM Symposium on Discrete Algorithms, 1999. · C.H. Papadimitriou, P. Raghavan, H. Tamaki, and S. Vempala, Latent Semantic Indexing: A Probabilistic Analysis, Proceedings of the ACM SIGACTSIGMODSIGART Symposium on Principles of Database Systems, 1998. · J. Kleinberg, C. Papadimitriou, and P. Raghavan, On the Value of Private Information, Proceedings of the Conference on Theoretical Aspects of Rationality and Knowledge, 2001.
Lecture 17 (12/6/2005)
Summary: Discussed the auction mechanisms currently used to sell advertisement auctions on the Internet (sponsored search), and challenges involved in the design of better mechanisms. Presented three recent results on auctions for budgetconstrained bidders, bid optimization in advertisement auctions, and online revenuemaximizing auctions for perishable items with unknown supply.
Recommended reading: · C. Borgs, J. Chayes, N. Immorlica, M. Mahdian, and A. Saberi, Multiunit auctions with budgetconstrained bidders, ACM Conference on Electronic Commerce, 2005. · C. Borgs, J. Chayes, O. Etesami, N. Immorlica, K. Jain, and M. Mahdian, Bid optimization in online advertisement auctions, manuscript, 2005. · M. Mahdian, and A. Saberi, Multiunit auctions with unknown supply, manuscript, 2005.
Other references: · N. Immorlica, K. Jain, M. Mahdian, and K. Talwar, Click Fraud Resistant Methods for Learning ClickThrough Rates, Workshop on Internet and Network Economics (WINE), 2005. · H. Bhargava, J. Feng, and D. Pennock , Implementing Sponsored Search in Web Search Engines: Computational Evaluation of Alternative Mechanisms, forthcoming in Informs Journal on Computing, 2006. · H. Bhargava, and J. Feng, Paid placement strategies for internet search engines, WWW 2002. · B. Edelman, M. Ostrovsky, and M. Schwarz, Internet Advertising and the Generalized Second Price Auction: Selling Billions of Dollars Worth of Keywords, Stanford Graduate School of Business Research Paper #1917, 2005. · J. Goodman, Payperpercentage of Impressions: An Advertising Method that is Highly Robust to Fraud, Presented at the ACM ECommerce Workshop on Sponsored Search Auctions, June 2005. · A. Mehta, A. Saberi, U. Vazirani, and V. Vazirani, Adwords and Generalized Online Matching, FOCS 2005.
Lecture 18 (12/8/2005)
Summary: Finished the discussion of advertisement auctions (revenuemaximizing auctions with unknown supply), and concluded the course with a discussion of some of the challenging open problems related to the topics presented in this course.
