Computer Science 789
Topics: Online Algorithms
Spring 2009
Assignments and Lecture Topics

Revised May 3, 2009

Handouts

Here are the most recent versions of the handouts:

Section 1: Feb 24 14:01: Probabilities and Expected Values. in postscript form pdf form
Section 2: Feb 24 13:59: Competitive Analysis. in postscript form pdf form
Section 3: Feb 24 13:59: Potentials. in postscript form pdf form
Section 4: Feb 24 13:59: Bookmark Algorithms for Paging. in postscript form pdf form
Section 5: Feb 24 13:58: Metrical Task Systems. in postscript form pdf form
Section 6: Mar 10 08:19: Metric Spaces. in postscript form pdf form
Section 7: Mar 3 09:48: The Server Problem. in postscript form pdf form
Section 8: Feb 26 11:29: Randomized Online Algorithms for the Server Problem. in postscript form pdf form
Section 9: Mar 17 08:18: EQUITABLE: A Randomized Paging Algorithm. in postscript form pdf form
Section 10: Mar 24 11:43: The List Access Problem. in postscript form pdf form
Section 11: Apr 23 09:28: Knowledge State Algorithms for the Server Problem. in postscript form pdf form
Section 12: Apr 23 09:07: Trackless Algorithms for the Server Problem and Paging. in postscript form pdf form

T-Theory Applications to Online Algorithms for the Server Problem, an Arxiv file based on James Oravec's thesis.

Online Algorithms: A Survey, A survey of online algorithms by Susanne Albers.

The On-line K-Server Problem, a survey by Aris Floratos and Ravi Boppana

Tuesday, January 13, 2009

We will very briefly discuss online algorithms.

Today's handout in postscript form pdf form

Thursday, January 15, 2009

Today's handout in postscript form pdf form

Homework due. Numbers of exercises changed February 25

Why should we try to minimize competitiveness, instead of simply minimizing cost?
Consider the paging problem. If we are simply trying to minimize cost, the worst case is that there is a fault at every step. The adversary can easily guarantee that we pay at every step, by simply requesting a new page at every step. There is no way we can reduce the cost in that situation. Therefore, if our goal is simply to minimize the worst case cost, there is no point in worrying about paging strategy; any algorithm is just as good as any other.
On the other hand, remember that in the offline case, we are usually interested in minimizing the cost for the given inputs. That means, in the case of paging, that we would like to minimize the cost given a specific sequence of requests. An online algorithm cannot do this, so competitive analysis was invented as a way to measure how close the performance of an online algorithm is to this goal.

Tuesday, January 20, 2009

Today, I will prove that LRU is k-competitive for the k-paging problem.

I will also give a 3/2-competitive randomized algorithm for the 2-paging problem.

Thursday, January 22, 2009

Today we will primarily discuss the potential method.

Today's handout in postscript form pdf form

Tuesday, January 27, 2009

Today's handout in postscript form pdf form

Thursday, January 29, 2009

Homework due. Numbers of exercises changed February 25

Please read "Why Competitive Analysis," starting on page xiii of your textbook.

What is "Yao's principle"?

Today we will prove the lower bound of H_k for the competitiveness of any randomized algorithm for the k-paging problem. The proof makes use of the result of Exercise 1.13.

Metrical task systems and work functions, Chapter 9 of your textbook. A metrical task system (MTS) is very general; paging is an example of an MTS.

Tuesday, February 3, 2009

We will discuss work functions, offset functions, and how to use them to compute competitiveness.

Thursday, February 5, 2009

Tuesday, February 10, 2009

Today we will discuss work functions for the paging problem.

Thursday, February 12, 2009

Homework due. Numbers of exercises changed February 25

fig file

eps file

Today, we will find the randomized competitiveness of the Ice Cream problem, against the oblivious adversary.
Instead of simply telling you what the competitiveness is and then proving it, I will work it out in class. In order to play fair, I will deliberately refrain from computing it in advance or looking it up in my notes.
I might need your help!

Tuesday, February 17, 2009

I will review the homework that was turned in Thursday.

If time permits, I will introduce the k-server problem.

Thursday, February 19, 2009

Today, we will prove that there is no online algorithm for the $k$-server problem that it less than k-competitive on any metric space with more than $k$ points.

The k-server conjecture states that, for any metric space M, there is a k-competitive online algorithm for the k-server problem. This conjecture remains open in general, although it has been proved true in a number of special cases.

Tuesday, February 24, 2009

Thursday, February 26, 2009

Homework due.

The proof I gave in class of the 2-competitiveness of Random-Slack is only half done. I failed to consider the possibility that the minimum matching goes the other way.

Tuesday, March 3, 2009

Thursday, March 5, 2009

Tuesday, March 10, 2009

Thursday, March 12, 2009

Tuesday, March 17, 2009

Today I will continue discussion of EQUITABLE.

If time permits, I will introduce a new concept: heteroscopic online problems. Up to now, we have ignored this problem. Except for MARK, which is pretty trivial, all randomized online algorithms we have considered have been homoscopic. But real life online problems are usually heteroscopic.

Thursday, March 19, 2009

Homework due. Why?

WFA uses unbounded memory. Can you use forgiveness to decrease the memory requirement? Let's take another look at DC, with that question in mind.

At some point, we must return to the first online problem ever considered, the list accessing problem. I will start on this problem today.

Saturday, March 21, 2009

Preparation for Exam: postscript form pdf form

If there are any errors, contact me immediately.

Sun Mar 22 04:21:20 PDT 2009 I fixed an error.

Thursday, March 26, 2009

Examination today postponed.

Monday, March 30, 2009

Updated Exam (last update Mon Mar 30 04:27:05 PDT 2009 ): postscript form pdf form

No change in the questions, but just a smidge more information about the last problem.

If there are any errors, contact me immediately.

You wanted work functions, you got work functions.

Tuesday, March 31, 2009

Examination today.

Thursday, April 2, 2009

Tuesday, April 14, 2009

Trackless handout today: postscript form pdf form

Thursday, April 16, 2009

Trackless Server Problem Tutorial

Tuesday, April 21, 2009

Thursday, April 23, 2009

Tuesday, April 28, 2009

Thursday, April 30, 2009

Homework 6 due.

Homework 7 due.

Tuesday, May 5, 2009

Final Examination, 10:10 to 12:10. To be postponed if possible.

Friday, May 8, 2009

If I can get a room, the final examination will be 9:00 to 11:00 today.

Approximate final (as handed out Thursday, April 30, in class:
in postscript form
pdf form