Week 1

• Meeting 1: Stable Matching. Section 0.5 (lecture 0, Section 0.5) of Jeff Erickson's notes.
• Meeting 2: Implementation of the stable matching algorithm so that in runs in O(n^2) time. The Towers of Hanoi problem (Sections 1.2 and 1.3).

Week 2

• Meeting 1: Mergesort (1.4) and Quicksort (1.5).
• Meeting 2: Selection (1.7)

Week 3

• Meeting 1: Selection (1.7) and Integer Multiplication (1.8).
• Meeting 2:

Week 4

• Meeting 1: Completing the discussion of Integer Multiplication (1.8). The subset sum problem from Section 3.3.
• Meeting 2: Recursive thinking for the longest increasing subsequence (LIS) from Section 3.6. An efficient algorithm using memoization, and also via an iterative algorithm. This is from Section 5.2.

Week 5

• Meeting 1: Subset Sum -- memoization, and an iterative algorithm. See 5.6 for a brief summary.
• Meeting 2: Edit Distance from Section 5.5. The recursive thinking, followed by an iterative algorithm and example.

Week 6

• Meeting 1: The randomized protocol for contention resolution. This is not from Jeff Erickson's notes. See Files --> Handouts in ICON for posted notes.
• Meeting 2: Verifying Matrix Product. Also not from Jeff's notes. See Files --> Handouts in ICON for posted notes.

Week 7

• Meeting 1: Randomized minimum cut, from Lecture 14 of Jeff Erickson's notes.
• Meeting 2: Continuing with randomized minimum cut.

Week 8

• Meeting 1: Expectation, linearity, examples of expectation computation. Some of the examples we did can be found in Files --> Handouts --> Expectation and Median in ICON.
• Meeting 2: Analysis of expected running time of quicksort and the randomized slection algorithm. Notes in ICON.

Week 9

• Meeting 1: Expected running time of hash table operations, and universal hash function families. See Lecture 12 of Jeff's notes, and here for a more updated version.
• Meeting 2: An application of universal hash functions to estimating frequency of items in a data stream. See these notes from Jeff.

Week 10

• Meeting 1: A proof that the family MP is near-universal can also be found in Jeff's updated notes on hashing mentioned above in Week 9, Lecture 1. The proof I gave in class avoided the terminology of groups and inverses. The discussion of balls and bins and perfect hashing can be found in the sections `High probability bounds: balls and bins' and `Perfect Hashing' in these same notes.
• Meeting 2: Midterm.

Week 11

• Meeting 1: Maximum flows and minimum cuts, from Lecture 23 of Jeff's notes. Here are the slides we used.
• Meeting 2: Correctness of Ford-Fulkerson, running time with integer capacities, mention of the Edmonds-Karp rules and the running times they give. See Lecture 23.

Week 12

• Meeting 1: Application of Maximum Flow to Maximum Bipartite Matching. See Lecture 24 (Applications of Maximum Flow) of Jeff's notes.
• Meeting 2: A handout for the image segmentation application of minimum cuts is in ICON. The project selection application is in 24.6 of Jeff's lectures.

Week 13

• Meeting 1: Introduction the SAT and CNF-SAT problems. Reductions: LIS to longest path in DAGs.
• Meeting 2: The independent set problem, reduction of some problems, including maximum matching, to independent set. Reduction of CNF-SAT to independent set, covered in Lecture 30 of Jeff's notes. Defining polynomial-time (Cook) reducibility.

Week 14

• Meeting 1: Decision problems vs. Optimization problems. The classes P and NP, with examples. How to show that a problem belongs to NP. The P vs NP question.
• Meeting 2: Polynomial-time Karp reducibility, consequences, definitions of NP-hard and NP-complete, Cook-Levin Theorem, showing NP-completeness of Independent Set.