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Click on the theme item for the meeting plan for that theme.
Click on the meeting item for references, exercises, and additional reading related to it.
  • Theme 1 : Counting Complexity - 18 meetings

    • Meeting 01 : Mon, Jan 19, 08:00 am-08:50 am
      • Administrative Announcements. Overview of the course. Counting Complexity. Computational Model. The class FP. Clique vs #Clique Problem. Cycle vs #Cycle Problem. Decision vs Counting Problems. Counting the number of spanning trees in a given undirected graph. Kirchoff's Matrix Tree Theorem. The need of a theory.

    • Meeting 02 : Tue, Jan 20, 12:00 pm-12:50 pm
      • If #CYCLE is in FP, then P = NP. Discussion on #BPM problem. The Class #P. Closure properties.

    • Meeting 03 : Tue, Jan 27, 12:00 pm-12:50 pm
      • The bits and value of the #P function. Counting as a generalisation of NP, BPP, RP, PP and Parity P. NP is contained in PP. #P = FP if and only if PP = P.

    • Meeting 04 : Tue, Jan 27, 06:00 pm-06:50 pm
      • (Lecture on Jan 22nd, rescheduled to Jan 27, 6pm.)
      Notion of #P-completeness. Attempt 1 : Parsimonious reductions. #SAT is #P-complete. #IND-SET is #P-complete. Shortcomings of the theory. General oracle query model of #P-completeness. Valiant's theorem.

    • Meeting 05 : Wed, Jan 28, 06:00 pm-06:50 pm
      • (Lecture on Jan 22, rescheduled to Jan 28, 6 pm)
      Determinant and permanent. Combinatorial interpretation of 0-1 permanent in terms of perfect matchings. Combinatorial interpretations of permanent over integers via cycle covers in graphs with integer weights on edges. A useful trick of "cancellations" using negative weights.

    • Meeting 06 : Thu, Jan 29, 11:00 am-11:50 am
      • Permanent over Integers is #P-complete. Valiant's reduction.

    • Meeting 07 : Fri, Jan 30, 10:00 am-10:50 am
      • Permanent over {0,1} is #P-complete.

    • Meeting 08 : Mon, Feb 02, 08:00 am-08:50 am
      • To Be Announced

    • Meeting 09 : Tue, Feb 03, 12:00 pm-12:50 pm
      • To Be Announced

    • Meeting 10 : Thu, Feb 05, 11:00 am-11:50 am
      • To Be Announced

    • Meeting 11 : Thu, Feb 05, 06:30 pm-07:30 pm
      • To Be Announced

    • Meeting 12 : Mon, Feb 09, 08:00 am-08:50 am
      • To Be Announced

    • Meeting 13 : Tue, Feb 10, 12:00 pm-12:50 pm
      • To Be Announced

    • Meeting 14 : Thu, Feb 12, 11:00 am-11:50 am
      • To Be Announced

    • (Upcoming) Meeting 15 : Fri, Feb 13, 10:00 am-10:50 am
      • To Be Announced

    • (Upcoming) Meeting 16 : Mon, Feb 16, 08:00 am-08:50 am
      • To Be Announced

    • (Upcoming) Meeting 17 : Tue, Feb 17, 12:00 pm-12:50 pm
      • To Be Announced

    • (Upcoming) Meeting 18 : Thu, Feb 19, 11:00 am-11:50 am
      • To Be Announced

  • Theme 2 : Circuit Complexity - 18 meetings
  • Theme 3 : Hardness vs Randomness - 10 meetings
  • Theme 4 : Interactive Proofs - 12 meetings