4005-801: Homework, slides, and other materials


Week 1

• Slides for this week: Introduction - pdf (and ppt)


• Tuesday, Mar 13
  • Covered in class: Course logistics, see the main course website
  • Covered in class: introduction to Markov chains, examples, formal definition
  • A note for students with disabilities: RIT is committed to providing reasonable accommodations to students with disabilities. If you would like to request accommodations such as special seating, testing modifications, or note taking services due to a disability, please contact the Disability Services Office. It is located in the Eastman Building, Room 2342; the Web site is www.rit.edu/dso. After you receive accommodation approval, it is imperative that you see me during office hours so that we can work out whatever arrangement is necessary.


• Thursday, Mar 15
  • Covered in class: stationary distribution, aperiodity, irreducibility, Gambler's Ruin (most of Chapter 1 and started Chapter 2 of the LPW book)


• Homework 1, due 3/22 4:00pm (in class): pdf

• Slides for this week: Hitting, Commute, and Cover Time - pdf (and ppt)
  


• Tuesday, Mar 20
  • Note about Problem 1 on Hw1: consider all possible card decks as Omega. For fun (i.e., you do not have to submit this part), do the posted MC move with probability 1/2 and otherwise flip the order of the top two cards.
  • Covered in class: Coupon Collector, mixing time of a random walk on a hypercube (Chapter 2 of LPW)


• Thursday, Mar 22
  • Covered in class: estimating the likelihood of being more than cn steps beyond the expectation for the Coupon Collector problem
  • Covered in class: revisited random walks on graphs, their stationary distribution
  • Covered in class: definitions of hitting, commute, and cover time
  • Covered in class: hitting time via a system of linear equations
  • Covered in class: started electrical networks (in class distributed copies of pages 135-138 of Raghavan&Motwani's Randomized Algorithms book)


• Homework 2, due 3/29 2:00pm (in class): pdf

• Slides for this week: Chapters 3 and 4 (except Section 3.2): Mixing Time and Coupling - pdf (and ppt)


• Tuesday, Mar 27
  • Covered in class: expressing commute time via effective resistance and its applications (Motwani-Raghavan)
  • Covered in class: solutions of Hw 1


• Thursday, Mar 29
  • Covered in class: cover time <= n^3 (Motwani-Raghavan)
  • Covered in class: total variation distance and the definition of the mixing time, detailed balance condition and Metropolis filter (Sections 3.1 and 3.3)
  • Covered in class: solutions of Hw 2


• Homework 3, due 4/5 2:00pm (in class): pdf
  

• Slides for this week: we'll continue with last week's slides


• Tuesday, Apr 3
  • Covered in class: coupling (Chapter 4)


• Thursday, Apr 5
  • Covered in class: the coupling argument applied to the coloring Markov chain (Chapter 4 - we will finish the path coupling part next week)
  • Possible presentation topics:
    • Stopping heuristics for Markov chains (a survey of several stopping heuristics - how to determine whether a MC has reached its stationary distribution)
    • The simulated annealing technique - we will probably not have time to cover this before week 8, I would like to see this covered during student presentations
    • Practical applications of Markov chains (choose one and tell us about it) - I would like to see some involving the simulated annealing heuristics
    • Torpidly mixing Markov chains (Markov chains that do not mix/converge quickly - possibly requiring exponential time to mix)
    • #P-complete problems, including not too complicated (but not trivial either) reductions
    • Deterministic counting algorithms
    • Randomized algorithms (including those that do not use Markov chains)
    The first two topics are well described in Markov Chain Monte Carlo in Practice, a book owned by the RIT library. There are other interesting topics in the book, if you would prefer to pick one of those.
    The other topics are more open-ended, where you search for a problem on your own. (Come talk to me if you'd like me to help you find a suitable problem.)
    Other logistics about the presentations:
    • Your presentation will last about 25 minutes, with about 5 minutes for questions. You might join forces and prepare a 50-minute joint presentation where both presenters equally contribute to the preparation and the presentation.
    • The presentations take place in weeks 9 and 10. We will have 4 presentations per class.
    • You are free to choose between preparing slides or presenting your topic using the whiteboard. If you choose whiteboard, prepare a summary handout of your topic. I will post the slides and the handouts on this website.
    • Recall that presentations are worth 25% of the final grade. This will be broken into 70% for your presentation and 30% for participation in other students presentations. In particular, you get full 30% if you ask a relevant question every presentation day and if a relevant question is asked of every presenter.


• Homework 4, due 4/16 10:00am: pdf (due to delayed posting, I am extending the deadline until Monday morning - feel free to slide your homework submission under my office door if I am not around)
  

• Slides for this week: Section 3.2: Sampling and Counting - pdf (ppt)


• Tuesday, April 10
  • Covered in class: path coupling
  • Covered in class: Markov and Chebyshev's inequality


• Thursday, April 12
  • Covered in class: using sampling to count (Section 3.2)
  • Covered in class: solutions of Hw3


• Homework 5, due 4/23 10:00am: pdf
  

• Slides for this week: we continued with last week's slides, then Chapter 5: Canonical Paths - pdf (ppt) and the demo - pdf (ppt)


• Tuesday, Apr 17
  • The project has been posted.
  • Reminder: Notify me of your presentation topic choice by the end of week 6.
  • Covered in class: continued the sampling to counting reduction


• Thursday, Apr 19
  • Covered in class: the last step of the sampling to counting reduction
  • Covered in class: Canonical Paths (Chapter 5)
  • Covered in class: solutions of Hw 4


• Homework 6, due 4/30 10:00am: pdf
  

• Slides for this week: Chapter 1: Deterministic counting algorithms - pdf (ppt)


• Tuesday, Apr 24
  • Covered in class: canonical paths applied to matchings
  • Covered in class: deterministic counting algorithms: counting via dynamic programming, sampling via counting



• Thursday, Apr 26
  • Covered in class: sampling via counting revisited - dynamic programming and Kasteleyn's Theorem
  • Covered in class: solutions of problem 1 on Hw 5
  • Exam information can be found here.

• Tuesday, May 1
  • Covered in class: solutions of Hw 6, problem 2 on Hw 5, and revisiting Hw 4
  • Covered in class: sketch of the connection between the determinant and counting perfect matchings in a Pfaffian-oriented graph



• Thursday, May 3
  • In class: exam.

• Tue Week 9
  • Ben Mayes: #P-completeness 1 (introduction, permanent to perfect matchings in bipartite graphs reduction) - presentation
  • Zach Langley: #P-completeness 2 (sketch of the proof that permanent is #P-complete, weighted matchings to weighted perfect matchings in bipartite graphs reduction) - presentation
  • Max Bogue: Particle filters - presentation
  
  
• Thu Week 9
  • Brian Leibig: Simulated annealing and its applications 1 (0-1 Knapsack) - presentation
  • James Loomis: Simulated annealing and its applications 2 (Circuit design) - presentation
  • Okka Kyaw: using Markov chains to analyze a board game (Monopoly) - presentation
  • Josh Lindsay: Hidden Markov Model - presentation
  
  
• Tue Week 10
  • Anuj Panwar: Randomized algorithms 1 (finding a pair of closest points in the plane) - presentation
  • Alex Lange: Randomized algorithms 2 - presentation
  • Tony Bentancur: Markov decision processes - presentation
  • Ragdeep Moturu: Simulated annealing and its applications 3 (Traveling Salesman Problem) - presentation
  
  
• Thu Week 10
  • Gopinath Vasalamarri: #P-completeness 3 (counting all possible topological orderings of a dag)
  • Matt Au: Phylogeny or protein folding
  • David Stalnaker: Deterministic counting algorithms
  
  
• After seeing all the presentations, please rate them here. The survey is open until the end of the day on Saturday, May 19, 2012.