If you want to choose onf of these topics, to know more about it, or to suggest a new topic not listed here please talk to me.

• Randomized Rounding
  • R. Motwani, J. Naor, and P. Raghavan,
    Randomized Approximation Algorithms in Combinatorial Optimization,
    In Approximation Algorithms for NP-hard Problems (Boston, MA, 1997), D. Hochbaum, ed., PWS Publishing, pp. 144--191.
• Approximating arbitrary metrics by tree metrics and low-stretch spanning trees:
  • Jittat Fakcharoenphol, Satish Rao, Kunal Talwar,
    A tight bound on approximating arbitrary metrics by tree metrics,
    Proceedings of the thirty-fifth annual ACM symposium on Theory of computing (STOC'03)
  • Michael Elkin, Yuval Emek, Daniel A. Spielman, Shang-Hua Teng,
    Lower-stretch spanning trees,
    Proceedings of the thirty-seventh annual ACM symposium on Theory of computing, (STOC'05)
  • Y. Bartal,
    Probabilistic approximation of metric spaces and its algorithmic applications,
    Proceedings of the 37th Annual Symposium on Foundations of Computer Science, p.184, October 14-16, FOCS, 1996.
  • Yair Bartal,
    On approximating arbitrary metrices by tree metrics,
    Proceedings of the thirtieth annual ACM symposium on Theory of computing, STOC (1998) p.161-168, May 24-26.
• Rapidly mixing markov chains
  • Mark Jerrum and Alistair Sinclair,
    The Markov chain Monte Carlo method: an approach to approximate counting and integration,
    A survey paper as a chapter in Approximation Algorithms for NP-hard Problems, (Dorit Hochbaum, ed.), PWS, 1996.
  • Mike Molloy,
    "The Glauber dynamics on the colourings of a graph with large girth and maximum degree",
    SIAM J. Computing (to appear). Conference version in Proceedings of STOC 2002. (can be downloaded from Mike's webpage)
  • Alan Frieze and Eric Vigoda,
    "A survey on the use of Markov chains to randomly sample colorings"
    downloadable from Alan's homepage.
  • M. Dyer, A. Frieze, T. Hayes and E. Vigoda
    "Randomly coloring constant degree graphs",
    In proceedings of FOCS (complete version downloadable from Alan's homepage).
• Applications of Probabilistic method in graph coloring (the Psuedo-random coloring method).
  See me for some references.
• Streaming
  • Goedel Prize winning paper by Alon, Matias, Szegedy,
    "The Space Complexity of Approximating the frequency moments",
    in J. of computer and system sciences (JCSS), 1996.
  • Mayur Datar, Aristides Gionis, Piotr Indyk, Rajeev Motwani,
    "Maintaining Stream Statistics over Sliding Windows",
    in SIAM J. Computing, V31(6), pp 1794-1813, 2002.
  • P. Indyk, D. Woodruff,
    "Optimal approximations of the frequency moments of data streams"
    in Proc. of STOC 2005.
• Some of the applications of the LLL
  • N. Alon, A. Bar Noy, N. Linial and D. Peleg,
    On the complexity of radio communication,
    Proc. 21th ACM Symp. on the Theory of Computing (STOC), Seattle, Washington, ACM Press (1989), 274-285.
  • N. Alon, C. McDiarmid, B. Reed,
    Acyclic coloring of graphs,
    Random Structures and Algorithms, 2(3):277-288, 1991.
  • U. Feige and C. Scheideler,
    Improved bounds for acyclic job shop scheduling
    In STOC 1998.
• Property testing
  • O. Goldreich, S. Goldwasser and D. Ron,
    "Property testing and its connection to learning and approximation".
    JACM, 1998.
  • Dana Ron,
    "Property testing",
    a survey downloadable from Citeseer.
  • Noga Alon and Asaf Shapira,
    "Every Monotone Graph Property is Testable",
    in Proc. of STOC 2005, 128-137. (downloadable from Noga's webpage)
• Volume estimation
  • Martin Dyer, Alan Frieze, Ravi Kannan,
    "A random polynomial-time algorithm for approximating the volume of convex bodies",
    JACM 38, pp 1-17, 1991