Unless otherwise specified, all readings are in MotwaniRaghavan. As always, the future is uncertain, so you should take parts of the schedule that haven't happened yet with a grain of salt.

# 1. Detailed schedule

- 2009-01-12
RandomizedAlgorithms. What they are and what we will do with them. Readings: §§1.1–1.2, 1.5.

- 2009-01-14
ProbabilisticRecurrences. Readings: §1.4.

- 2009-01-16
RandomizedLowerBounds: minimax principles and Yao's lemma, Adleman's theorem. Readings: §2.1–2.2.

- 2009-01-21
Derandomization and Adleman's theorem. Start of ProbabilisticInequalities: Markov's inequality and Chebyshev's inequality. Readings: §2.3, §§3.1–3.3.

- 2009-01-23
**Make-up lecture in AKW 200.**More ProbabilisticInequalities: Chernoff bounds. Readings: §4.1.- 2009-01-26
Guest lecture by NicholasRuozzi: randomized rounding and set cover; examples of the ProbabilisticMethod (max-SAT, independent sets). Readings: §§5.1–5.2.

- 2009-01-28
Review session by NicholasRuozzi.

- 2009-02-02
Martingales: basics. Readings: §4.4.

- 2009-02-04
Martingales: how zero-mean martingales act like sums of independent random variables. The Azuma-Hoeffding inequality and the method of bounded differences.

- 2009-02-09
Martingales and stopping times. The optional stopping theorem.

- 2009-02-11
More Martingales: submartingales and supermartingales.

- 2009-02-16
MarkovChains: definition, classification of states, convergence. Readings: §§6.1–6.2.

- 2009-02-18
More MarkovChains: Bounding convergence rates using the coupling method. Readings: Chapter 4-3 of the Aldous-Fill manuscript.

- 2009-02-23
Reversible MarkovChains.

- 2009-02-25
More reversible MarkovChains: Conductance and canonical paths.

- 2009-03-02
Still more MarkovChains: Path coupling, sampling, counting using graph coloring as an example. Side note: The Boyd-Vandenberghe convex optimization book mentioned in class can be found at http://www.stanford.edu/~boyd/cvxbook/. Readings: MitzenmacherUpfal §§11.5–11.6.

- 2009-03-04
MarkovChain Monte Carlo optimization: The Metropolis-Hastings algorithm and simulated annealing. Readings: MitzenmacherUpfal §10.4.

- 2009-03-23
The JohnsonLindenstraussTheorem and applications. Readings: Mostly we will be doing the proof in this paper by Dasgupta and Gupta.

- 2009-03-25
Randomized data structures: RandomizedSearchTrees, skip lists. Readings: §§8.1–8.3.

- 2009-03-30
More randomized data structures: HashTables. Readings: §§8.4–8.5.

- 2009-04-01
Fancier HashTables: cuckoo hashing and Bloom filters. Readings: Pagh and Rodler, Cuckoo hashing (see HashTables page for downloadable version), MitzenmacherUpfal §5.5.3.

- 2009-04-06
KwiseIndependence, plus a quick refresher on FiniteFields. Readings: MitzenmacherUpfal §13.1–13.2.

- 2009-04-08
DataStreamComputation. Readings: MitzenmacherUpfal §13.4.

- 2009-04-13
Start of OnLineAlgorithms: The list update problem. Readings: Chapter 13.

- 2009-04-15
More OnLineAlgorithms: Paging.

- 2009-04-20
Randomized distributed algorithms; RandomizedConsensus. Readings: see notes.

- 2009-04-22
BalancedAllocations. Readings: MitzenmacherUpfal Chapter 14.

The **final exam** was given Monday, 2009-05-11, starting at 2:00pm in AKW 500. It was a closed-book test covering all material discussed during the semester. final-2009.pdf, final-2009-solutions.pdf